Q&A Hero

Q: In testing the equality of population variances, two assumptions are required: independent samples and normally distributed populations.

Q: The controller of a chain of toy stores is interested in determining whether there is any difference in the weekly sales of store 1 and store 2. The weekly sales are normally distributed. This problem should be analyzed using an independent means method.

Q: When we are testing a hypothesis about the difference in two population proportions based on large independent samples, we compute a combined (pooled) proportion from the two samples if we assume that there is no difference between the two proportions in our null hypothesis.

Q: If the limits of the confidence interval of the difference between the means of two normally distributed populations were from -2.6 to 1.4 at the 95 percent confidence level, then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

Q: If the limits of the confidence interval of the difference between the means of two normally distributed populations were 8.5 and 11.5 at the 95 percent confidence level, then we can conclude that we are 95 percent certain that there is a significant difference between the two population means.

Q: Assume that we are constructing a confidence interval for the difference in the means of two populations based on independent random samples. If both sample sizes and=10, and the distributions of both populations are highly skewed, then a confidence interval for the difference in the means can be constructed using the t test statistic.

Q: When comparing two population means based on independent random samples, the pooled estimate of the variance is used when there is an assumption of equal population variances.

Q: In testing the difference between the means of two independent populations, if neither population is normally distributed, then the sampling distribution of the difference in means will be approximately normal, provided that the sum of the sample sizes obtained from the two populations is at least 30.

Q: In testing the difference between the means of two normally distributed populations using independent random samples, we can only use a two-sided test.

Q: In testing the difference between the means of two normally distributed populations using independent random samples, the alternative hypothesis always indicates no differences between the two specified means.

Q: In testing the difference between the means of two normally distributed populations using large independent random samples, the sample sizes from the two populations must be equal.

Q: Consider an engine parts supplier, and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s2 = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. Using the upper end of the 95 percent confidence interval for and assuming that = 2.5, determine whether 99.73 percent of the outside diameters produced by the new machine are within the specification limits.

Q: Consider an engine parts supplier, and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s2 = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. Find the 95 percent confidence intervals for 2 and for the new machine.

Q: Consider an engine parts supplier, and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s2 = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. If 2 denotes the variance of the population of all outside diameters that would be produced by the new machine, test H0: 2 = .00075 versus Ha: 2 < .00075 by setting = .05.

Q: Consider an engine parts supplier, and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s2 = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. Assuming normality, determine whether 99.73 percent of the outside diameters produced by the current machine are within specification limits.

Q: A baker must monitor the temperature at which cookies are baked. Too much variation will cause inconsistency in the texture of the cookies. Past records show that the variance of the temperatures has been 1.44 degrees. A random sample of 30 batches of cookies is selected, and the sample variance of the temperature is 4.41 degrees. Test the hypothesis that the temperature variance has increased above 1.44 degrees at = .05.

Q: A baker must monitor the temperature at which cookies are baked. Too much variation will cause inconsistency in the texture of the cookies. Past records show that the variance of the temperatures has been 1.44 degrees. A random sample of 30 batches of cookies is selected, and the sample variance of the temperature is 4.41 degrees. What is the 95 percent confidence interval for 2 at = .05?

Q: A baker must monitor the temperature at which cookies are baked. Too much variation will cause inconsistency in the texture of the cookies. Past records show that the variance of the temperatures has been 1.44 degrees. A random sample of 30 batches of cookies is selected, and the sample variance of the temperature is 4.41 degrees. What is the test statistic for testing the null hypothesis that the population variance has increased above 1.44 degrees?

Q: In a sample of n = 16 selected from a normally distributed population, we find a population standard deviation of s = 10. What is the value of x2 if we are testing H0: 2 = 144?

Q: A manufacturer of an automobile part has a process that is designed to produce the part with a target of 2.5 inches in length. In the past, the standard deviation of the length has been 0.035 inches. In an effort to reduce the variation in the process, the manufacturer has redesigned the process. A sample of 25 parts produced under the new process shows a sample standard deviation of 0.025 inches. Test the claim that the new process standard deviation has improved from the current process at = .05.

Q: A manufacturer of an automobile part has a process that is designed to produce the part with a target of 2.5 inches in length. In the past, the standard deviation of the length has been 0.035 inches. In an effort to reduce the variation in the process, the manufacturer has redesigned the process. A sample of 25 parts produced under the new process shows a sample standard deviation of 0.025 inches. Calculate the test statistic for testing whether the new process standard deviation has improved from the current process.

Q: If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. What is the p-value associated with the test statistic calculated to test the claim that less than 40 percent of the county residents are protected by earthquake insurance?

Q: If you live in California, the decision to buy earthquake insurance is an important one. A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance. Calculate the appropriate test statistic to test the claim that less than 40 percent of the residents in the county are protected by earthquake insurance.

Q: A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot. A wine producer in California, where merlot is produced, believes the figure is higher in California. She contacts a random sample of 550 California residents and asks which wine they purchase most often. Suppose 115 reply that merlot is the primary wine. Using the p-value rule, calculate the p-value associated with the test statistic, and test the claim at = .01.

Q: A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot. A wine producer in California, where merlot is produced, believes the figure is higher in California. She contacts a random sample of 550 California residents and asks which wine they purchase most often. Suppose 115 reply that merlot is the primary wine. Calculate the appropriate test statistic to test the hypotheses.

Q: Failure to meet payments on student loans guaranteed by the US government has been a major problem for both banks and the government. Approximately 50 percent of all student loans guaranteed by the government are in default. A random sample of 350 loans to college students in one region of the United States indicates that 147 are in default. Calculate the p-value associated with the test statistic, and , using the p-value rule, test the hypothesis that the default rate for the selected region is lower than the national percentage at = .01.

Q: Failure to meet payments on student loans guaranteed by the US government has been a major problem for both banks and the government. Approximately 50 percent of all student loans guaranteed by the government are in default. A random sample of 350 loans to college students in one region of the United States indicates that 147 are in default. Calculate the appropriate test statistic to test the hypothesis that the default rate for the selected region is lower than the national percentage.

Q: Last year, TV station KAAA had a share of the 6 p.m. news audience approximately equal to, but not greater than, 25 percent. The advertising department for the station believes the current audience share is higher than the 25 percent share they had last year. In an attempt to substantiate this belief, the station surveyed a random sample of 400 viewers of 6 p.m. news and found that 146 watched KAAA. Test these hypotheses at = .001 using the critical value rule.

Q: Last year, TV station KAAA had a share of the 6 p.m. news audience approximately equal to, but not greater than, 25 percent. The advertising department for the station believes the current audience share is higher than the 25 percent share they had last year. In an attempt to substantiate this belief, the station surveyed a random sample of 400 viewers of 6 p.m. news and found that 146 watched KAAA. Calculate the appropriate test statistic to test the hypotheses using the critical value rule.

Q: In an early study, researchers at Ivy University found that 33 percent of the freshmen had received at least one A in their first semester. Administrators are concerned that grade inflation has caused this percentage to increase. In a more recent study, of a random sample of 500 freshmen, 185 had at least one A in their first semester. Calculate the p-value associated with the test statistic and test the claim at = .05 using the p-value rule.

Q: In an early study, researchers at Ivy University found that 33 percent of the freshmen had received at least one A in their first semester. Administrators are concerned that grade inflation has caused this percentage to increase. In a more recent study, of a random sample of 500 freshmen, 185 had at least one A in their first semester. Calculate the appropriate test statistic to test the hypotheses.

Q: A sample of 400 journalism majors at a major research university was asked if they agreed with the following statement: "Government should be more involved in the oversight and regulation of reporting." Fifty-two percent of the respondents agreed with the statement. Calculate the p-value associated with the test statistic and test at = .05 using the p-value rule.

Q: A sample of 400 journalism majors at a major research university was asked if they agreed with the following statement: "Government should be more involved in the oversight and regulation of reporting." Fifty-two percent of the respondents agreed with the statement. Calculate the appropriate test statistic to test the claim that at least 50 percent of journalism majors agree with the statement.

Q: In 1930, the average size of a public restroom was 172 square feet. By 1990, due to federal disability laws, the average size had increased to 471 square feet. Suppose that a design team believes that this standard has increased from the 1990 level. They randomly sample 23 public restrooms in a major midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94. Test the hypotheses at = .001 using the critical value rule.

Q: In 1930, the average size of a public restroom was 172 square feet. By 1990, due to federal disability laws, the average size had increased to 471 square feet. Suppose that a design team believes that this standard has increased from the 1990 level. They randomly sample 23 public restrooms in a major midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94. Calculate the appropriate test statistic to test the hypotheses.

Q: According to a national survey, the average commuting time for people living in a city with a population of 1 to 3 million is 19.0 minutes. Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim for her city. Taking a random sample of 20 commuters, she calculates a mean time of 19.346 minutes and a standard deviation of 2.842 minutes. Test the hypotheses at = .10 using the critical value rule.

Q: According to a national survey, the average commuting time for people living in a city with a population of 1 to 3 million is 19.0 minutes. Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim for her city. Taking a random sample of 20 commuters, she calculates a mean time of 19.346 minutes and a standard deviation of 2.842 minutes. Calculate the appropriate test statistic to test the hypotheses.

Q: A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards. The mean emission of all converters of this type must be less than 20 parts per million of carbon monoxide. Ten (10) converters are manufactured for testing purposes and their emission levels are measured, with a mean of 17.17 and a standard deviation of 2.98. Test the hypotheses at = .01 using the critical value rule.

Q: A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards. The mean emission of all converters of this type must be less than 20 parts per million of carbon monoxide. Ten (10) converters are manufactured for testing purposes and their emission levels are measured, with a mean of 17.17 and a standard deviation of 2.98. Calculate the appropriate test statistic to test the hypotheses using the critical value rule.

Q: In a bottling process, a manufacturer will lose money if the bottles contain either more or less than is claimed on the label. Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant-size bottle differs from the labeled amount of 20 ounces. The manager samples nine bottles, measures their contents, and finds the sample mean is 19.7 ounces and the sample standard deviation is 0.3 ounces. Test the hypotheses at = .05 using the critical value rule.

Q: In a bottling process, a manufacturer will lose money if the bottles contain either more or less than is claimed on the label. Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant-size bottle differs from the labeled amount of 20 ounces. The manager samples nine bottles, measures their contents, and finds the sample mean is 19.7 ounces and the sample standard deviation is 0.3 ounces. Calculate the appropriate test statistic to test the hypotheses using the critical value rule.

Q: The manager of a local specialty store is concerned with a possible slowdown in payments by her customers. She measures the rate of payment in terms of the average number of days receivables are outstanding. Generally, the store has maintained an average of 50 days with a standard deviation of 10 days. A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days. Calculate the appropriate test statistic to apply the critical value rule.

Q: Last year, during an investigation of the time spent reading emails on a daily basis, researchers found that on Monday the average time was 50 minutes. Office workers claim that with the increased spam and junk mail, this time has now increased. To conduct a test, a sample of 25 employees is selected, with the following results: sample mean = 51.05 minutes and sample standard deviation = 14.2 minutes. What is the critical value for = .05 to test the hypotheses and apply the critical value rule to determine if the null hypothesis can be rejected.

Q: Last year, during an investigation of the time spent reading emails on a daily basis, researchers found that on Monday the average time was 50 minutes. Office workers claim that with the increased spam and junk mail, this time has now increased. To conduct a test, a sample of 25 employees is selected, with the following results: sample mean = 51.05 minutes and sample standard deviation = 4.42 minutes. Calculate the appropriate test statistic to apply the critical value rule on the hypothesis that the time has increased from last year.

Q: The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test her theory, she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. She finds a sample mean of 61.35. Assume a population standard deviation of 4.45. If we want the probability of a Type I error and Type II error to be equal to .05, what is the sample size needed to make both the probability of a Type I error and the probability of a Type II error as small as possible. (Assume an alternative value of the population mean of 61.) The claim is that the tablet count is different from 60.

Q: The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test her theory, she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. She finds a sample mean of 61.35. Assume a population standard deviation of 4.45. If we have preset the probability of a Type I error equal to .05, compute the probability of a Type II error. (Assume an alternative value of the population mean of 61.) The claim is that the tablet count is different from 60.

Q: The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test her theory, she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. She finds a sample mean of 62.05 and a standard deviation of 4.45. Calculate a confidence interval to test the hypotheses at = .002 and interpret the result.

Q: The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription. The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions. To test her theory, she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle. She finds a sample mean of 62.05 and a standard deviation of 4.45. Calculate the test statistic for using the critical value rule testing that the number of tablets is significantly different from 60.

Q: A cereal manufacturer is concerned that the boxes of cereal not be underfilled or overfilled. Each box of cereal is supposed to contain 13 ounces of cereal. A random sample of 31 boxes is tested. The average weight is 12.58 ounces, and the standard deviation is 0.25 ounces. Calculate a confidence interval to test the hypotheses at = .10 and interpret.

Q: A cereal manufacturer is concerned that the boxes of cereal not be underfilled or overfilled. Each box of cereal is supposed to contain 13 ounces of cereal. A random sample of 31 boxes is tested. The average weight is 12.58 ounces, and the standard deviation is 0.25 ounces. What is the critical value for testing the hypotheses at = .001.

Q: A cereal manufacturer is concerned that the boxes of cereal not be underfilled or overfilled. Each box of cereal is supposed to contain 13 ounces of cereal. A random sample of 31 boxes is tested. The average weight is 12.58 ounces, and the standard deviation is 0.25 ounces. Calculate the test statistic to use in applying the critical value rule to test the hypotheses.

Q: It has been hypothesized that on average employees spend one hour a day playing video games at work. To test this at her company, a manager takes a random sample of 35 employees, who showed a mean time of 55 minutes per day with an assumed population standard deviation of 5 minutes. Calculate a confidence interval to test the hypotheses that the employees spend a different amount of time from one hour (60 minutes) at = .02 and interpret.

Q: It has been hypothesized that on average employees spend one hour a day playing video games at work. To test this at her company, a manager takes a random sample of 35 employees, who showed a mean time of 55 minutes per day with an assumed population standard deviation of 5 minutes. What is the critical value for testing these hypotheses at = .01?

Q: It has been hypothesized that, on average, employees spend one hour a day playing video games at work. To test this at her company, a manager takes a random sample of 35 employees, who showed a mean time of 55 minutes per day, with an assumed population standard deviation of 5 minutes. Calculate the test statistic.

Q: The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon. It is known from the specifications that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 32 bottles is selected, and the mean amount of water per 1-gallon bottle is found to be 0.995 gallon. Calculate a confidence interval to test the hypotheses at = .001 and determine whether the specifications are being met.

Q: The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon. It is known from the specifications that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 32 bottles is selected, and the mean amount of water per 1-gallon bottle is found to be 0.995 gallon. Calculate the p-value and test whether the specifications are being met at = .001 using the p-value rule.

Q: The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually averages 1 gallon. It is known from the specifications that the standard deviation of the amount of water is equal to 0.02 gallon. A random sample of 32 bottles is selected, and the mean amount of water per 1-gallon bottle is found to be 0.995 gallon. Calculate the test statistic.

Q: A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The standard deviation of the process is 0.15 ounces. A sample of 48 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces. Calculate a confidence interval to test the hypotheses at = .05 and determine if the process should be stopped.

Q: A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The standard deviation of the process is 0.15 ounces. A sample of 48 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces. Calculate the p-value and determine if the process is working properly when testing at = .10 using the p-value rule.

Q: A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressing is working properly when 8 ounces are dispensed. The standard deviation of the process is 0.15 ounces. A sample of 48 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces. Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces. Calculate the test statistic.

Q: It is estimated that the average person in the United States uses 123 gallons of water per day. Some environmentalists believe this figure is too high and conduct a survey of 40 randomly selected Americans. They find a mean of 113.03 gallons and a population standard deviation of 25.99 gallons. Calculate the p-value for this test statistic, and test the hypothesis at = .01 using the p-value rule.

Q: It is estimated that the average person in the United States uses 123 gallons of water per day. Some environmentalists believe this figure is too high and conduct a survey of 40 randomly selected Americans. They find a mean of 113.03 gallons and a population standard deviation of 25.99 gallons. Calculate the appropriate test statistic to test the hypotheses using the critical value rule.

Q: Standard X-ray machines should give radiation dosages below 5.00 milliroentgens (mR). To test a certain X-ray machine, a sample of 36 observations is taken, with a mean of 4.13 mR and a population standard deviation of 1.91 mR. Calculate the p-value for this test statistic and test the claim at = .05 using the p-value rule.

Q: Standard X-ray machines should give radiation dosages below 5.00 milliroentgens (mR). To test a certain X-ray machine, a sample of 36 observations is taken, with a mean of 4.13 mR and a population standard deviation of 1.91 mR. Calculate the appropriate test statistic to test the hypotheses using the critical value rule.

Q: In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles. Calculate the p-value corresponding to the test statistic used to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles and, applying the p-value rule, determine if the null hypothesis can be rejected at = .01.

Q: In a study of distances traveled by buses before the first major engine failure, a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles. Calculate the appropriate test statistic to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

Q: A company has developed a new ink-jet cartridge for its printer that it believes has a longer lifetime on average than the one currently being produced. To investigate its length of life, 240 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages, respectively. The historical average lifetime for cartridges produced by the current process is 1502.5 pages. At = .05, test the claim that the new cartridge has a longer lifetime using the critical value rule.

Q: A company has developed a new ink-jet cartridge for its printer that it believes has a longer lifetime on average than the one currently being produced. To investigate its length of life, 40 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages, respectively. The historical average lifetime for cartridges produced by the current process is 1502.5 pages. Calculate the appropriate test statistic to test the hypotheses using the critical value rule.

Q: The manufacturer of an over-the-counter heartburn relief mediation claims that its product brings relief in less than 3.5 minutes, on average. To be able to make this claim, the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes. Calculate the p-value that corresponds to the test statistic that would be used in applying the p-value rule.

Q: The manufacturer of an over-the-counter heartburn relief mediation claims that its product brings relief in less than 3.5 minutes, on average. To be able to make this claim, the manufacturer was required by the FDA to present statistical evidence in support of the claim. The manufacturer reported that for a sample of 50 heartburn sufferers, the mean time to relief was 3.3 minutes and the population standard deviation was 1.1 minutes. Calculate the appropriate test statistic to test the hypotheses when using the critical value rule.

Q: A random sample of 80 companies who announced corrections to their balance sheets took a mean time of 8.1 days for the time between balance sheet construction and the complete audit. The population standard deviation is assumed to be 1.3 days . What is the critical value for = .001 to apply the critical value rule for the claim that is greater than 7.5 days?

Q: A random sample of 80 companies who announced corrections to their balance sheets took a mean time of 8.1 days for the time between balance sheet construction and the complete audit. The population standard deviation is assumed to be 1.3 days. If the claim is that the population mean is greater than 7.5 days, calculate the appropriate test statistic to test the hypotheses.

Q: A mail-order business prides itself in its ability to fill orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a population standard deviation of 1.5 days. What is the critical value for = .10 when using the critical value rule to test the hypothesis that the time to fill orders is less than 6 days?

Q: A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. On one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a population standard deviation of 1.5 days. Calculate the appropriate test statistic to test the hypotheses.

Q: A major airline company is concerned that its proportion of late arrivals has substantially increased in the past month. Historical data shows that on average 18 percent of the company airplanes have arrived late. In a random sample of 1,240 airplanes, 310 airplanes have arrived late. If we are conducting a hypothesis test using the critical value rule to determine if the proportion of late arrivals has increased, what is the value of the calculated test statistic?

Q: A null hypothesis H0: 2.4 is not rejected at a significance level of 0.04 ( = 0.04). The standard deviation for the normally distributed population is known to be 0.40. Determine the probability of a Type II error, if we assume that the actual mean is 2.125 based on a sample size of 16.

Q: Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. What is the p-value that would be used in applying the p-value rule?

Q: Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. What is the value of the test statistic to test the claim?

Q: Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. What is the critical value to test the claim at = .01?

Q: Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. What is the critical value used to test the claim at = .05?