Q&A Hero

Q: The results of recent polls on presidential approval ratings are shown below.Approved of President in JanuaryApproved of President in JulyYesYesYesYesNoNoNoYesNoYesYesNoNoNoNoYesNoNoNoYesNoYesYesNoNoYesNoYesNoNoYesYesNoNoYesNoYesYesNoYesNoNoNoYesNoNoNoNoNoNoNoNoYesNoYesYesNoYesYesNoDoes the data provide sufficient evidence to conclude that the presidential approval ratings differ between the two months? Use Excel to conduct the appropriate test at = .05.

Q: A company gives a test to prospective employees before granting an interview. A researcher hypothesizes that men tend to answer one particular test question correctly more often than women. Independent samples of both groups are given the test. The results for the question of interest follow. Does the data provide sufficient evidence to conclude that the proportion of correct answers given by men is greater than that of women? Use Excel to conduct the appropriate test at = .05.MenWomenYesYesYesYesNoNoYesYesNoYesYesNoYesNoNoYesNoNoNoYesNoYesYesNoYesYesNoYesNoNoYesYesNoNoYesNoNoYesNoYesNoNoNoYesNoNoNoNoYesNoNoNoYesNoNoYesNoYesYesNo

Q: A manufacturing company wants to estimate the difference in the proportion of defective parts between two machines. Independent random samples of parts are taken from both machines. The results follow. Use Excel to estimate the difference in the proportion of defective parts between two machines with a 99% level of confidence.Machine 1Machine 2YesYesNoNoNoNoNoYesNoNoYesNoNoNoNoNoNoNoNoYesNoNoNoNoNoNoNoYesNoNoNoNoNoNoYesNoNoNoNoYesNoNoNoYesNoNoNoNoNoNoNoNoYesNoNoNoNoYesNoNo

Q: The data below represents the fields of specialization for a randomly selected sample of undergraduate students. We want to determine whether there is a significant difference in the fields of specialization between regions of the country.NortheastMidwestSouthWestTotalBusiness54652893240Engineering152483380Liberal Arts65843398280Fine Arts131572560Health Sciences3124214015020080270700a. Determine the critical value of the chi-square (c2) for this test of independence.b. Calculate the value of the test statistic.c. What is the conclusion for this test? Let a= .05.

Q: From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations.Level of EducationHigh SchoolBachelorGraduateTotalPublic Broadcasting110190100400Commercial Stations80220100400Total190410200800Test at a= .05 to determine if the selection of a TV station is dependent upon the level of education. Use the p-value approach.

Q: Two hundred fifty managers with degrees in business administration indicated their fields of concentration as shown below.MajorTop ManagementMiddle ManagementTotalManagement6560125Marketing302050Accounting255075Total120130250At a= .01 using the p-value approach, test to determine if the position in management is independent of the major of concentration.

Q: A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Rights Amendment. The following contingency table shows the results of the votes:SexFavorUndecidedOpposeTotalFemale1808040300Male1502030200Total33010070500At a= .05 using the p-value approach, test to determine if the votes cast were independent of the sex of the individuals.

Q: Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile. The results are given below.StylingEngineeringFuel EconomyTotalMale70130150350Female3020100150100150250500a. State the null and alternative hypotheses for a contingency table test.b. State the decision rule for the critical value approach. Let a= 0.10.c. Calculate the c2test statistic.d. Give your conclusion for this test.

Q: Dr. Sherri Brock's diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where some individuals took the diet pills and some did not.Diet PillsNo Diet PillsTotalNo Weight Loss8020100Weight Loss100100200Total180120300We want to see if losing weight is independent of taking the diet pills.a. Compute the test statistic.b. Using the p-value approach at 95% confidence, test to determine if weight loss is independent on taking the pill.c. Use the critical method approach and test for independence.

Q: A group of 2000 individuals from 3 different cities were asked whether they owned a foreign or a domestic car. The following contingency table shows the results of the survey.CityType of CarDetroitAtlantaDenverTotalDomestic80200520800Foreign1206004801200Total20080010002000At a= 0.05 using the p-value approach, test to determine if the type of car purchased is independent of the city in which the purchasers live.

Q: A sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. Their incomes were categorized as follows.Category 1 $20,000 up to $40,000Category 2 $40,000 up to $60,000Category 3 $60,000 up to $80,000The results of the survey are shown below.Income CategoryMaleFemaleCategory 11030Category 23515Category 31545We want to determine if yearly income is independent of gender.a. Compute the test statistic.b. Using the p-value approach, test to determine if yearly income is independent of gender.

Q: Shown below is 2 x 3 contingency table with observed values from a sample of 500. At 95% confidence using the critical value approach, test for independence of the row and column factors. Column Factor Row Factor X Y Z A 40 50 110 B 60 100 140

Q: Shown below is 3 x 2 contingency table with observed values from a sample of 1,500. At 95% confidence, test for independence of the row and column factors. Column Factor Row Factor X Y Total A 450 300 750 B 300 300 600 C 100 50 150 Total 850 650 1,500

Q: The following table shows the results of a recent study regarding the gender of individuals and their selected field of study.Field of StudyMaleFemaleTotalMedicine8040120Business602080Engineering16040200Total300100400We want to determine if the selected field of study is independent of gender.a. Compute the test statistic.b. Using the p-value approach at 90% confidence, test to see if the field of study is independent of gender.c. Using the critical method approach at 90% confidence, test for the independence of major and gender.

Q: The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old.a. State the null and alternative hypotheses to be tested.b. Compute the test statistic.c. The null hypothesis is to be tested at the 1% level of significance. Determine the critical value from the table.d. What do you conclude?

Q: A lottery is conducted that involves the random selection of numbers from 0 to 4. To make sure that the lottery is fair, a sample of 250 was taken. The following results were obtained.ValueFrequency040145255360450a. State the null and alternative hypotheses to be tested.b. Compute the test statistic.c. The null hypothesis is to be tested at the 5% level of significance. Determine the critical value from the table.d. What do you conclude about the fairness of this lottery?

Q: A major automobile manufacturer claimed that the frequencies of repairs on all five models of its cars are the same. A sample of 200 repair services showed the following frequencies on the various makes of cars.Model of CarFrequencyA32B45C43D34E46At a= 0.05, test the manufacturer's claim.

Q: Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With a= 0.05, test to see if the methods of payment have changed during the Christmas rush.

Q: In the last presidential election before the candidates began their major campaigns, the percentages of registered voters who favored the various candidates were as follows.PercentageRepublicans34Democrats43Independents23After the major campaigns began, a random sample of 400 voters showed that 172 favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64 favored the Independent candidate. Test with a= .01 to see if the proportion of voters who favored the various candidates changed.

Q: In 2003, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2004, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see whether there has been a significant change in the proportions between 2003 and 2004.

Q: The personnel department of a large corporation reported sixty resignations during the last year. The following table groups these resignations according to the season in which they occurred. Season Number of Resignations Winter 10 Spring 22 Summer 19 Fall 9 Test to see if the number of resignations is uniform over the four seasons. Let a= 0.05.

Q: Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major:

Q: Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates would be as follows.PercentageDemocrats48%Republicans38%Independents4%Undecided10%After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. We want to see if the proportion of voters has changed.a. Compute the test statistic.b. Use the p-value approach to test the hypotheses. Let a= .05.c. Using the critical value approach, test the hypotheses. Let a= .05.

Q: A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week.DayCardiac DeathsMonday40Tuesday17Wednesday16Thursday29Friday15Saturday20Sunday17We want to determine whether the number of deaths is uniform over the week.a. Compute the test statistic.b. Using the p-value approach at 95% confidence, test for the uniformity of death over the week.c. Using the critical value approach, perform the test for uniformity.

Q: Before the start of the Winter Olympics, it was expectedthat the percentages of medals awarded to the top contenders to be as follows.PercentagesUnited States25%Germany22%Norway18%Austria14%Russia11%France10%Midway through the Olympics, of the 120 medals awarded, the following distribution was observed.Number of MedalsUnited States33Germany36Norway18Austria15Russia12France6We want to test to see if there is a significant difference between the expected and actual awards given.a. Compute the test statistic.b. Using the p-value approach, test to see if there is a significant difference between the expected and the actual values. Let a= .05.c. At 95% confidence, test for a significant difference using the critical value approach.

Q: A school administrator believes that there is no difference between student dropout rate for schools located in rural areas and schools located in urban areas. A random sample of 100 schools in the rural areas was taken. The student dropout rate of the schools in the sample was 27%. A random sample of 80 schools in the urban areas had a dropout rate of 20%.a. Give a point estimate for the difference between the population proportions for the two districts.b. Give a point estimate of the standard deviation for the difference between the population proportions.c. Compute the test statistic for testing the administrator's belief.d. At 95% confidence using the p-value approach, test the administrator's belief.

Q: The results of a recent poll on the preference of voters regarding presidential candidates are shown below.CandidateVoters SurveyedVoters Favoring This CandidateA400192B450225At 95% confidence, test to determine whether or not there is a significant difference between the preferences for the two candidates.

Q: The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials.a. Give a point estimate for the difference between the population proportions of these machines.b. Calculate the pooled estimate of the population proportion.c. Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance.

Q: The office of records at a university has stated that the proportion of incoming female students who major in business has increased. A sample of female students taken several years ago is compared with a sample of female students this year. Results are summarized below. Has the proportion increasedsignificantly? Test at alpha = .10.Sample SizeNo. Majoring in BusinessPrevious Sample (p)25075Current Sample (c)30069

Q: In a sample of 100 Republicans, 60 favored the President's anti-drug program. While in a sample of 150 Democrats, 84 favored his program. At 95% confidence, test to see if there is a significant difference in the proportions of the Democrats and the Republicans who favored the President's anti-drug program.

Q: A comparative study of organic and conventionally grown produce checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic versus conventionally grown produce? Test at = 0.10.Sample SizeE. Coli PrevalenceOrganic2003Conventional50020

Q: During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi.StateVoters SurveyedVoters Favoring the Democratic CandidateAlabama800440Mississippi600360a. We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states. Provide the hypotheses.b. Compute the test statistic.c. Determine the p-value; and at 95% confidence, test the above hypotheses.

Q: Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president.a. Compute the test statistic.b. At alpha = .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.)

Q: A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five ago. Results are summarized below. Has the proportion increasedsignificantly? Let a= 0.05.Sample SizeNumber Considered Themselves OverweightCurrent Sample (c)300150Previous Sample (p)275121

Q: From production line A, a sample of 500 items is selected at random; and it is determined that 30 items are defective. In a sample of 300 items from production process B (which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportions of defectives in the two lines.

Q: In a random sample of 200 Republicans, 160 opposed the new tax laws. While in a sample of 120 Democrats, 84 opposed the new tax laws. Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats opposed to this new law.

Q: The results of a recent poll on the preference of voters regarding the presidential candidates are shown below.Voters SurveyedVoters Favoring This CandidateCandidate A200150Candidate B300195a. Develop a 90% confidence interval estimate for the difference between the proportions of voters favoring each candidate.b. Does your confidence interval provide conclusive evidence that one of the candidates is favored more?Explain.

Q: In a sample of 40 Democrats, 6 opposed the President's foreign policy, while of 50 Republicans, 8 were opposed to his policy. Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Q: During the primary elections of 2004, candidate A showed the following pre-election voter support in Tennessee and Mississippi.Voters SurveyedVoters Favoring Candidate ATennessee500295Mississippi700357a. Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states.b. Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes, which state?Explain.

Q: Of 150 Chattanooga residents surveyed, 60 indicated that they participated in a recycling program. In Knoxville, 120 residents were surveyed and 36 claimed to recycle.a. Determine a 95% confidence interval estimate for the difference between the proportions of residents recycling in the two cities.b. From your answer in Part a, is there sufficient evidence to conclude that there is a significant difference in the proportion of residents participating in a recycling program?

Q: Among a sample of 50 MDs (medical doctors) in the city of Memphis, Tennessee, 10 indicated they make house calls; while among a sample of 100 MDs in Atlanta, Georgia, 18 said they make house calls. Determine a 95% interval estimate for the difference between the proportions of doctors who make house calls in the two cities.

Q: Of 200 UTC seniors surveyed, 60 were planning on attending Graduate School. At UTK, 400 seniors were surveyed; and 100 indicated that they were planning to attend Graduate School.a. Determine a 95% confidence interval estimate for the difference between the proportions of seniors at the two universities that were planning to attend Graduate School.b. Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK?Explain.

Q: Babies weighing less than 5.5 pounds at birth are considered "low-birth-weight babies." In the United States, 7.6% of newborns are low-birth-weight babies. The following information was accumulated from samples of new births taken from two counties.HamiltonShelbySample size150200Number of "low-birth-weight babies1822a. Develop a 95% confidence interval estimate for the difference between the proportionsof low-weight babies in the two counties.b. Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county?Explain, using the results of Part a. Do not perform any test.

Q: Refer to Exhibit 11-8. The p-value isa. between .1 and .05b. between .05 and .025c. between .025 and .01d. less than 0.005

Q: Refer to Exhibit 11-8. The test statistic for this test of independence is a. 0 b. 8.4 c. 62.5 d. 82.5

Q: Refer to Exhibit 11-8. The expected number of adults who prefer coffee is a. 0.25 b. 0.33 c. 150 d. 200

Q: Exhibit 11-8The table below gives beverage preferences for random samples of teens and adults.TeensAdultsTotalCoffee50200250Tea100150250Soft Drink200200400Other50501004006001,000We are asked to test for independence between age (i.e., adult and teen) and drink preferences.Refer to Exhibit 11-8. With a .05 level of significance, the critical value for the test isa. 1.645b. 7.815c. 14.067d. 15.507

Q: Refer to Exhibit 11-7. The conclusion of the test is that thea. proportions have changed significantlyb. proportions have not changed significantlyc. test is inconclusived. None of these alternatives is correct.

Q: Refer to Exhibit 11-7. The p-value is a. greater than 0.1 b. between 0.05 and 0.1 c. between 0.025 and 0.05 d. between 0.01 and .025

Q: Refer to Exhibit 11-7. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals a. 1.645 b. 1.96 c. 5.991 d. 7.815

Q: Refer to Exhibit 11-7. The calculated value for the test statistic equals a. 0.01 b. 0.75 c. 4.29 d. 4.38

Q: Refer to Exhibit 11-7. The expected frequency for the Business College is a. 0.3 b. 0.35 c. 90 d. 105

Q: Exhibit 11-7In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.Refer to Exhibit 11-7. This problem is an example of aa. normally distributed variableb. test for independencec. Poisson distributed variabled. multinomial population

Q: Refer to Exhibit 11-6. The p-value isa. less than .005b. between .005 and .01c. between .01 and .025d. between .025 and .05

Q: Refer to Exhibit 11-6. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals a. 3.84 b. 7.81 c. 5.99 d. 9.34

Q: Refer to Exhibit 11-6. The number of degrees of freedom associated with this problem is a. 4 b. 149 c. 1 d. 3

Q: Refer to Exhibit 11-6. The test statistic is a. 10.08 b. 54.02 c. 1.96 d. 1.645

Q: Exhibit 11-6In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.Patients CuredPatients Not CuredReceived medication7010Received sugar pills2050We are interested in determining whether or not the medication was effective in curing the common cold.Refer to Exhibit 11-6. The expected frequency of those who received medication and were cured isa. 70b. 150c. 28d. 48

Q: Refer to Exhibit 11-5. At 95% confidence, the null hypothesisa. should not be rejectedb. should be rejectedc. was designed wrongd. None of these alternatives is correct.

Q: Refer to Exhibit 11-5. The p-value is a. less than .005 b. between .025 and 0.05 c. between .05 and 0.1 d. greater than 0.1

Q: Refer to Exhibit 11-5. The calculated value for the test statistic equals a. 0.5444 b. 300 c. 1.6615 d. 6.6615

Q: Refer to Exhibit 11-5. The expected frequency of seniors is a. 60 b. 20% c. 68 d. 64

Q: Exhibit 11-5Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.Freshmen83Sophomores68Juniors85Seniors64We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.Refer to Exhibit 11-5. The expected number of freshmen isa. 83b. 90c. 30d. 10

Q: Refer to Exhibit 11-4. The conclusion of the test (at 95% confidence) is that thea. distribution is uniformb. distribution is not uniformc. test is inconclusived. None of these alternatives is correct.

Q: Refer to Exhibit 11-4. The p-value is a. larger than 0.1 b. less than 0.1 c. less than 0.05 d. larger than 0.9

Q: Refer to Exhibit 11-4. The number of degrees of freedom associated with this problem is a. 150 b. 149 c. 2 d. 3

Q: Refer to Exhibit 11-4. The calculated value for the test statistic equals a. 2 b. -2 c. 20 d. 4

Q: Exhibit 11-4When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.Do you supportNumber ofcapital punishment?individualsYes40No60No Opinion50We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.Refer to Exhibit 11-4. The expected frequency for each group isa. 0.333b. 0.50c. 1/3d. 50

Q: Refer to Exhibit 11-3. The 95% confidence interval for the difference between the two proportions isa. 384 to 450b. 0.48 to 0.5c. 0.028 to 0.068d. -0.068 to 0.028

Q: Refer to Exhibit 11-3. The standard error of is a. 0.48 b. 0.50 c. 0.03 d. 0.0243

Q: Exhibit 11-3The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.Music TypeTeenagers SurveyedTeenagers Favoring This TypePop800384Rap900450Refer to Exhibit 11-3. The point estimate for the difference between the proportions isa. -0.02b. 0.048c. 100d. 66

Q: Refer to Exhibit 11-2. The p-value isa. less than 0.001b. more than 0.10c. 0.0228d. 0.3

Q: Refer to Exhibit 11-2. The test statistic is a. 0.96 b. 1.96 c. 2.96 d. 3.96

Q: Refer to Exhibit 11-2. The pooled proportion is a. 0.305 b. 0.300 c. 0.027 d. 0.450

Q: Exhibit 11-2An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.Under Age of 18Over Age of 18n1 = 500n2 = 600Number of accidents = 180Number of accidents = 150We are interested in determining if the accident proportions differ between the two age groups.Refer to Exhibit 11-2 and let pUrepresent the proportion under and pOthe proportion over the age of 18. The null hypothesis isa. pU-pO0b. pU-pO0c. pU-pO0d. pU-pO= 0

Q: Refer to Exhibit 11-1. The 95% confidence interval estimate for the difference between the populations favoring the products isa. -0.024 to 0.064b. 0.6 to 0.7c. 0.024 to 0.7d. 0.02 to 0.3

Q: Refer to Exhibit 11-1. At 95% confidence, the margin of error is a. 0.064 b. 0.044 c. 0.0225 d. 52

Q: Refer to Exhibit 11-1. The standard error of is a. 52 b. 0.044 c. 0.0225 d. 100

Q: Exhibit 11-1The results of a recent poll on the preference of shoppers regarding two products are shown below.Shoppers FavoringProductShoppers SurveyedThis ProductA800560B900612Refer to Exhibit 11-1. The point estimate for the difference between the two population proportions in favor of this product isa. 52b. 100c. 0.44d. 0.02

Q: The degrees of freedom for a contingency table with 10 rows and 11 columns isa. 100b. 110c. 21d. 90