Q&A Hero

Q: A useful graph in almost any regression analysis is a scatterplot of residuals (on the vertical axis) versus fitted values (on the horizontal axis), where a "good" fit not only has small residuals, but it has residuals scattered randomly around zero with no apparent pattern.

Q: The least squares line is the line that minimizes the sum of the residuals.

Q: The residual is defined as the difference between the actual and predicted, or fitted values of the response variable.

Q: Correlation is measured on a scale from 0 to 1, where 0 indicates no linear relationship between two variables, and 1 indicates a perfect linear relationship.

Q: Correlation is used to determine the strength of the linear relationship between an explanatory variable X and response variable Y.

Q: When the scatterplot appears as a shapeless swarm of points, this can indicate that there is no relationship between the response variable Y and the explanatory variable X, or at least none worth pursuing.

Q: An outlier is an observation that falls outside of the general pattern of the rest of the observations on a scatterplot.

Q: Scatterplots are used for identifying outliers and quantifying relationships between variables.

Q: To help explain or predict the response variable in every regression study, we use one or more explanatory variables. These variables are also called response variables or independent variables.

Q: In every regression study there is a single variable that we are trying to explain or predict. This is called the response variable or dependent variable.

Q: Regression analysis can be applied equally well to cross-sectional and time series data.

Q: Cross-sectional data are usually data gathered from approximately the same period of time from a cross-sectional of a population.

Q: The two primary objectives of regression analysis are to study relationships between variables and to use those relationships to make predictions.

Q: Which of the following is an example of a nonlinear regression model? a. A quadratic regression equation b. A logarithmic regression equation c. Constant elasticity equation d. The learning curve model e. All of these options

Q: In linear regression, we can have an interaction variable. Algebraically, the interaction variable is theother variables in the regression equation. a. sum b. ratio c. product d. mean

Q: In linear regression, a dummyvariable is used: a. to represent residual variables b. to represent missing data in each sample c. to include hypothetical data in the regression equation d. to include categorical variables in the regression equation e. when "dumb" responses are included in the data

Q: The adjusted R2 adjusts R2 for: a. non-linearity b. outliers c. low correlation d. the number of explanatory variables in a multiple regression model

Q: An important condition when interpreting the coefficient for a particular independent variable X in a multiple regression equation is that: a. the dependent variable will remain constant b. the dependent variable will be allowed to vary c. all of the other independent variables remain constant d. all of the other independent variables be allowed to vary

Q: In multiple regression, the coefficients reflect the expected change in: a. Y when the associated X value increases by one unit b. X when the associated Y value increases by one unit c. Y when the associated X value decreases by one unit d. X when the associated Y value decreases by one unit

Q: In multiple regression, the constant : a. Is the expected value of the dependent variable Y when all of the independent variables have the value zero b. Is necessary to fit the multiple regression line to set of points c. Must be adjusted for the number of independent variables d. All of these options

Q: The regression line has been fitted to the data points (28, 60), (20, 50), (10, 18), and (25, 55). The sum of the squared residuals will be: a. 20.25 b. 16.00 c. 49.00 d. 94.25

Q: Given the least squares regression line, a. the relationship between X and Y is positive b. the relationship between X and Y is negative c. as X increases, so does Y d. as X decreases, so does Y e. there is no relationship between X and Y

Q: In a simple linear regression analysis, the following sums of squares are produced: The proportion of the variation in Y that is explained by the variation in X is: a. 20% b. 80% c. 25% d. 50% e. None of the above

Q: The percentage of variation (R2) ranges froma. 0 to +1b. -1 to +1c. -2 to +2d. -1 to 0

Q: The percentage of variation () can be interpreted as the fraction (or percent) of variation of the a. explanatory variable explained by the independent variable b. explanatory variable explained by the regression line c. response variable explained by the regression line d. error explained by the regression line

Q: Approximately what percentage of the observed Y values are within on standard error of the estimate () of the corresponding fitted Y values? a. 67% b. 95% c. 99% d. It is not possible to say

Q: A multiple regression analysis including 50 data points and 5 independent variables results in 40. The multiple standard error of estimate will be: a. 0.901 b. 0.888 c. 0.800 d. 0.953 e. 0.894

Q: The standard error of the estimate () is essentially the a. mean of the residuals b. standard deviation of the residuals c. mean of the explanatory variable d. standard deviation of the explanatory variable

Q: In choosing the "best-fitting" line through a set of points in linear regression, we choose the one with the: a. smallest sum of squared residuals b. largest sum of squared residuals c. smallest number of outliers d. largest number of points on the line e. None of these options

Q: In linear regression, the fitted value is the: a. predicted value of the dependent variable b. predicted value of the independent value c. predicted value of the slope d. predicted value of the intercept e. None of these options

Q: In linear regression, we fit the least squares line to a set of values (or points on a scatterplot). The distance from the line to a point is called the: a. fitted value b. residual c. correlation d. covariance e. None of these options

Q: The weakness of scatterplots is that they: a. do not help identify linear relationships b. can be misleading about the types of relationships they indicate c. only help identify outliers d. do not actually quantify the relationships between variables

Q: The term autocorrelation refers to: a. the analyzed data refers to itself b. the sample is related too closely to the population c. the data are in a loop (values repeat themselves) d. time series variables are usually related to their own past values

Q: A single variable X can explain a large percentage of the variation in some other variable Y when the two variables are: a. mutually exclusive b. inversely related c. directly related d. highly correlated e. None of the above

Q: The covariance is not used as much as the correlation because a. is not always a valid predictor of linear relationships b. it is difficult to calculate c. it is difficult to interpret d. all of these options

Q: The correlation value ranges from a. 0 to +1 b. "1 to +1 c. "2 to +2 d. " to+

Q: A correlation value of zero indicates. a. a strong linear relationship b. a weak linear relationship c. no linear relationship d. a perfect linear relationship

Q: Correlation is a summary measure that indicates: a. a curved relationship among the variables b. the rate of change in Y for a one unit change in X c. the strength of the linear relationship between pairs of variables d. the magnitude of difference between two variables

Q: A scatterplot that appears as a shapeless mass of data points indicates: a. a curved relationship among the variables b. a linear relationship among the variables c. a nonlinear relationship among the variables d. no relationship among the variables

Q: A "fan" shape in a scatterplot indicates: a. unequal variance b. a nonlinear relationship c. the absence of outliers d. sampling error

Q: Outliers are observations that a. lie outside the sample b. render the study useless c. lie outside the typical pattern of points on a scatterplot d. disrupt the entire linear trend

Q: ______ is/are especially helpful in identifying outliers.a. Linear regressionb. Regression analysisc. Normal curvesd. Scatterplotse. Multiple regression

Q: In regression analysis, which of the following causal relationships are possible? a. X causes Y to vary b. Y causes X to vary c. Other variables cause both X and Y to vary d. All of these options

Q: In regression analysis, if there are several explanatory variables, it is called: a. simple regression b. multiple regression c. compound regression d. composite regression

Q: In regression analysis, the variable we are trying to explain or predict is called the a. independent variable b. dependent variable c. regression variable d. statistical variable e. residual variable

Q: In regression analysis, the variables used to help explain or predict the response variable are called the a. independent variables b. dependent variables c. regression variables d. statistical variables

Q: Regression analysis asks: a. if there are differences between distinct populations b. if the sample is representative of the population c. how a single variable depends on other relevant variables d. how several variables depend on each other

Q: Data collected from approximately the same period of time from a cross-section of a population are called: a. time series data b. linear data c. cross-sectional data d. historical data

Q: The null hypothesis usually represents the: a. theory the researcher would like to prove. b. preconceived ideas of the researcher c. perceptions of the sample population d. status quo

Q: Which of the following statements are true of the null and alternative hypotheses? a. Exactly one hypothesis must be true b. Both hypotheses must be true c. It is possible for both hypotheses to be true d. It is possible for neither hypothesis to be true

Q: An informal test for normality that utilizes a scatterplot and looks for clustering around a 45line is known as a(n): a. Lilliefors test b. empirical cumulative distribution function c. p-test d. quantile-quantile plot

Q: The value set for is known as: a. the rejection level b. the acceptance level c. the significance level d. the error in the hypothesis test

Q: A two-tailed test is one where: a. results in only one direction can lead to rejection of the null hypothesis b. negative sample means lead to rejection of the null hypothesis c. results in either of two directions can lead to rejection of the null hypothesis d. no results lead to the rejection of the null hypothesis

Q: The form of the alternative hypothesis can be: a. one-tailed b. two-tailed c. neither one nor two-tailed d. one or two-tailed

Q: Of type I and type II error, which is traditionally regarded as more serious? a. Type I b. Type II c. Type I and Type II are equally serious d. Neither Type I or Type II is serious and both can be avoided

Q: A type II error occurs when: a. the null hypothesis is incorrectly accepted when it is false b. the null hypothesis is incorrectly rejected when it is true c. the sample mean differs from the population mean d. the test is biased

Q: The chi-square goodness-of-fit test can be used to test for: a. significance of sample statistics b. difference between population means c. normality d. difference between population variances

Q: One-tailed alternatives are phrased in terms of: a. b. < or > c. = d.

Q: NARRBEGIN: SA_126_128The retailing manager of Meijer supermarket chain in Michigan wants to determine whether product location has any effect on the sale of children toys. Three different aisle locations are considered: front, middle, and rear. A random sample of 18 stores is selected, with 6 stores randomly assigned to each aisle location. The size of the display area and price of the product are constant for all the stores. At the end of one-month trial period, the sales volumes (in thousands of dollars) of the product in each store were as shown below:NARRBEGIN: SA_126_128The retailing manager of Meijer supermarket chain in Michigan wants to determine whether product location has any effect on the sale of children toys. Three different aisle locations are considered: front, middle, and rear. A random sample of 18 stores is selected, with 6 stores randomly assigned to each aisle location. The size of the display area and price of the product are constant for all the stores. At the end of one-month trial period, the sales volumes (in thousands of dollars) of the product in each store were as shown below:Front AisleMiddle AisleRear Aisle10.04.66.08.63.87.46.83.45.47.62.84.26.43.23.65.43.04.2NARREND(A) At the 0.05 level of significance, is there evidence of a significant difference in average sales among the various aisle locations?(B) If appropriate, which aisle locations appear to differ significantly in average sales? (Use = 0.05)(C) What should the retailing manager conclude? Fully describe the retailing manager's options with respect to aisle locations?

Q: NARRBEGIN: SA_123_125Joe owns a sandwich shop near a large university. He wants to know if he is serving approximately the same number of customers as his competition. His closest competitors are Bob and Ted. Joe decides to use a couple of college students to collect some data for him on the number of lunch customers served by each sandwich shop during a weekday. The summary data for two weeks (10 days) and output from an ANOVA analysis are shown below.Summary stats for samples Joe'sBob'sTed's Sample sizes101010 Sample means50.70046.20043.500 Sample standard deviations4.2444.4923.598 Sample variances18.01120.17812.944 Weights for pooled variance 0.3330.3330.333 Number of samples3 Total sample size30 Grand mean46.800 Pooled variance17.044 Pooled standard deviation4.128 One-way ANOVA Table SourceSSdfMSFp-value Between variation264.602132.307.7620.0022 Within variation460.202717.044 Total variation724.8029 Confidence Intervals for mean difference using 95% confidence levelDifferenceMean diffLowerUpperJoe's " Bob's4.500-0.282 9.282Joe's " Ted's7.200 2.41811.982Bob's " Ted's2.700-2.082 7.482NARREND(A) Are all three sandwich shops serving the same number of customers, on average, for lunch each weekday? Test the appropriate hypotheses at the 5% level of significance.(B) Explain why the weights for the pooled variance are the same for each of the samples.(C) Use the information related to the 95% confidence interval to explain how the number of customers Joe has each weekday compares to his competition.

Q: NARRBEGIN: NAR: SA_120_122Do graduates of undergraduate business programs with different majors tend to earn disparate starting salaries? Below you will find output from an ANOVA analysis for 32 randomly selected graduates with majors in accounting (Acct), marketing (Mktg), finance (Fin), and information systems (IS).Summary statistics for samples Acct.Sample sizes9Sample means32711.67Sample standard deviations2957.438Sample variances8746437.5Weights for pooled variance0.286 Number of samples4Total sample size32Grand mean31039.22Pooled variance5308612.5Pooled standard deviation2304.043One Way ANOVA table SourceSSdfMSFp-valueBetween variation1176098073392032697.3850.0009Within variation148641149285308612 Total variation26625095531 Confidence Intervals for DifferencesDifferenceMean diffLower limitUpper limitAcct. - Mktg.4874.1671263.6728484.661Acct. " Fin.2537.667-609.8905685.223Acct. - IS-157.619-3609.9123294.674Mktg. " Fin.-2336.500-5874.0481201.048Mktg. - IS-5031.786-8843.014-1220.557Fin. - IS-2695.286-6071.216680.644NARREND(A) Assuming that the variances of the four underlying populations are equal, can you reject at a 5% significance level that the mean starting salaries for all given business majors are the same? Explain why or why not?(B) Is there any reason to doubt the equal-variance assumption made in (A)? Support your answer.

Q: An insurance firm interviewed a random sample of 600 college students to find out the type of life insurance preferred, if any. The results are shown in the table below. Is there evidence that life insurance preference of male students is different than that of female students. Test at the 5% significance level. Insurance Preference GenderTermWhole LifeNo Insurance Male8030240350 Female5040160250 13070400600

Q: The number of cars sold by three salespersons over a 6-month period are shown in the table below. Use the 5% level of significance to test for independence of salespersons and type of car sold. Insurance Preference ChevroletFordToyota Ali159529Bill2081543Chad1341128 482131100

Q: A recent study of educational levels of 1000 voters and their political party affiliations in a Midwestern state showed the results given in the table below. Use = .10 and test to determine if party affiliation is independent of the educational level of the voters. Party Affiliation Educational LevelDemocratRepublicanIndependent Didn't Complete High School9580115290Has High School Diploma13585105325Has College Degree160105120385 3902703401000

Q: A sport preference poll yielded the following data for men and women. Use the 5% significance level and test to determine if sport preference and gender are independent. Sport Preference GenderBasketballFootballSoccer Men20253075 Women18121545 383745120

Q: A statistics professor has just given a final examination in his linear models course. He is particularly interested in determining whether the distribution of 50 exam scores is normally distributed. The data are shown in the table below. Perform the Lilliefors test. Report and interpret the results of the test.7771788384718182797173897475937488839082796273887676768084849170767468808792847980917469888483878272

Q: NARRBEGIN: SA_113_114An automobile manufacturer needs to buy aluminum sheets with an average thickness of 0.05 inch. The manufacturer collects a random sample of 40 sheets from a potential supplier. The thickness of each sheet in this sample is measured (in inches) and recorded. The information below are pertaining to the Chi-square goodness-of-fit test.Upper limitCategoryFrequencyNormalDistance measure0.030.031 1.9200.4410.04 0.03 but 0.0410 8.0740.4590.05 0.04 but 0.051314.9470.2540.06 0.05 but 0.061211.2180.055 >0.064 3.8420.007Test of normal fitChi-square statistic1.214p-value0.545NARREND(A) Are these measurements normally distributed? Summarize your results.(B) Are there any weaknesses or concerns about your conclusions in (A)? Explain

Q: NARRBEGIN: SA_110_112In a survey of 1,500 customers who did holiday shopping on line during the 2000 holiday season, 270 indicated that they were not satisfied with their experience. Of the customers that were not satisfied, 143 indicated that they did not receive the products in time for the holidays, while 1,197 of the customers that were satisfied with their experience indicated that they did receive the products in time for the holidays. The following complete summary of results were reported:Satisfied with their experienceYes(in time)No(not in time)TotalYes1,197331,230No127143270Total1,3241761,500NARREND(A) Is there a significant difference in satisfaction between those who received their products in time for the holidays, and those who did not receive their products in time for the holidays? Test at the 0.01 level of significance.(B) Find the p-value associated with the test in Question 110 and interpret its meaning.(C) Based on the results of (A) and (B), if you were the marketing director of a company selling products online, what would you do to improve the satisfaction of the customers?

Q: NARRBEGIN: SA_106_109Two teams of workers assemble automobile engines at a manufacturing plant in Michigan. A random sample of 145 assemblies from team 1 shows 15 unacceptable assemblies. A similar random sample of 125 assemblies from team 2 shows 8 unacceptable assemblies.NARREND(A) Construct a 90% confidence interval for the difference between the proportions of unacceptable assemblies generated by the two teams.(B) Based on the confidence interval constructed in (A), is there sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies?(C) Is there sufficient evidence to conclude, at the 10% significance level, that the two teams differ with respect to their proportions of unacceptable assemblies? Conduct the appropriate hypothesis test.(D) Calculate the p-value and explain how to use it for testing the null hypothesis of equal proportion.

Q: An investor wants to compare the risks associated with two different stocks. One way to measure the risk of a given stock is to measure the variation in the stock's daily price changes. The investor obtains a random sample of 20 daily price changes for stock 1 and 20 daily price changes for stock 2. These data are shown in the table below. Show how this investor can compare the risks associated with the two stocks by testing the null hypothesis that the variances of the stocks are equal. Use = 0.10 and interpret the results of the statistical test.DayPrice Changefor stock 1Price Change for stock 21 1.86 0.872 1.80 1.333 1.03-0.274 0.16-0.205-0.73 0.256 0.90 0.007 0.09 0.098 0.19-0.719-0.42-0.3310 0.56 0.1211 1.24 0.4312-1.16-0.2313 0.37 0.7014-0.52-0.2415-0.09-0.5916 1.07 0.2417-0.88 0.6618 0.44-0.5419-0.21 0.5520 0.84 0.08

Q: NARRBEGIN: SA_101_104A real estate agency wants to compare the appraised values of single-family homes in two cities in Michigan. A sample of 60 listings in Lansing and 99 listings in Grand Rapids yields the following results (in thousands of dollars):LansingBig Rapids191.33172.34s32.616.92n6099NARREND(A) Is there evidence of a significant difference in the average appraised values for single-family homes in the two Michigan cities? Use 0.05 level of significance.(B) Have any of the assumptions made in (A) been violated? Explain.(C) Construct a 95% confidence interval estimate of the difference between the population means of Lansing and Grand Rapids.(D) Explain how to use the confidence interval in (C) to answer (A).

Q: NARRBEGIN: SA_96_100Q-Mart is interested in comparing customers who used its own charge card with those who use other types of credit cards. Q-Mart would like to know if customers who use the Q-Mart card spend more money per visit, on average, than customers who use some other type of credit card. They have collected information on a random sample of 38 charge customers and the data is presented below. On average, the person using a Q-Mart card spends $192.81 per visit and customers using another type of card spend $104.47 per visit.Summary statistics for two samplesQ-MartOther ChargesSample sizes1325Sample means192.81104.47Sample standard deviations115.24371.139Test of difference = 0Sample mean difference88.34Pooled standard deviation88.323Std error of difference30.201t-test statistic2.925p-value0.006NARREND(A) Given the information above, what is and for this comparison? Also, does this represent a one-tailed or a two-tailed test? Explain your answer.(B) What are the degrees of freedom for the t-statistic in this calculation? Explain how you would calculate the degrees of freedom in this case.(C) What is the assumption in this case that allows you to use the pooled standard deviation for this test?(D) Using a 5% level of significance, is there sufficient evidence for Q-Mart to conclude that customers who use the Q-Mart card charge, on average, more than those who use another charge card? Explain your answer.(E) Using a 1% level of significance, is there sufficient evidence for Q-Mart to conclude that customers who use the Q-Mart card charge, on average, more than those who use another charge card? Explain your answer.

Q: NARRBEGIN: SA_92_95Do undergraduate business students who major in information systems (IS) earn, on average, higher annual starting salaries than their peers who major in marketing (Mktg)? To address this question with a statistical hypothesis test, a comparison should be done to determine whether the variances of annual starting salaries of the two types of majors are equal. Below you will find output from a test of 20 randomly selected IS majors and 20 randomly selected Mktg majors.Summary statistics for two samplesIS SalaryMktg SalarySample sizes2020Sample means30401.3527715.85Sample standard deviations1937.522983.39Test of difference 0 Results if Results if Sample mean difference2685.5Pooled standard deviation2515.41NAStd error of difference795.44795.44Degrees of freedom3833t-test statistic3.3763.376p-value0.00090.0009Test of equality of variancesRatio of sample variances2.371p-value0.034NARREND(A) Use the information above to perform the test of equal variance. Explain how the ratio of sample variances is calculated. What type of distribution is used to test for equal variances? Also, would you conclude that the variances are equal or not? Explain.(B) Based on your conclusion in (A), which test statistic should be used in performing a test for the existence of a difference between population means?(C) Using a 5% level of significance, is there sufficient evidence to conclude that IS majors earn, on average, a higher annual starting salaries than their peers who major in Mktg?(D) Using a 1% level of significance, is there sufficient evidence to conclude that IS majors earn, on average, a higher annual starting salaries than their peers who major in Mktg? Explain your answer.

Q: NARRBEGIN: SA_88_91The manager of a consulting firm in Lansing, Michigan, is trying to assess the effectiveness of computer skills training given to all new entry-level professionals. In an effort to make such an assessment, he administers a computer skills test immediately before and after the training program to each of 20 randomly chosen employees. The pre-training and post-training scores of these 20 individuals are shown in the table below.EmployeeScore beforeScore after162772637737483464885848068180754838618898180108688117593127178138682147484156586169089177281187190198586206692NARREND(A) Is this two-sample data or paired data. Explain your answer.(B) Specify an appropriate hypothesis test.(C) Using a 10% level of significance, do the given sample data support that the firm's training programs is effective in increasing the new employee's computer skills?(D) Using a 1% level of significance, do the given sample data support that the firm's training programs is effective in increasing the new employee's working knowledge of computing ?

Q: NARRBEGIN: SA_84_87The owner of a popular Internet-based auction site believes that more than half of the people who sell items on her site are women. To test this hypothesis, the owner sampled 1000 customers who sold items on her site and she found that 53% of the customers sampled were women. Some calculations are shown in the table belowSample proportion0.53Standard error of sample proportion0.01578Z test statistic1.9008p-value0.0287NARREND(A) If you were to conduct a hypothesis test to determine if greater than 50% of customers who use this Internet-based site are women, would you conduct a one-tail or a two-tail hypothesis test? Explain your answer, and state the appropriate null and alternative hypotheses.(B) How many customers out of the 1000 sampled must have been women in this case?(C) Using a 5% significance level, can the owner of this site conclude that women make up more than 50% of her customers? Explain your answer.(D) If you were to use a 1% significance level, would the conclusion from (C) change? Explain your answer.

Q: NARRBEGIN: SA_80_83A marketing research consultant hired by Coca-Cola is interested in determining if the proportion of customers who prefer Coke to other brands is over 50%. A random sample of 200 consumers was selected from the market under investigation, 55% favored Coca-Cola over other brands. Additional information is presented below.Sample proportion0.55Standard error of sample proportion0.03518Z test statistic1.4213p-value0.07761NARREND(A) If you were to conduct a hypothesis test to determine if greater than 50% of customers prefer Coca-Cola to other brands, would you conduct a one-tail or a two-tail hypothesis test? Explain your answer.(B) How many customers out of the 200 sampled must have favored Coke in this case?(C) Using a 5% significance level, can the marketing consultant conclude that the proportion of customers who prefer Coca-Cola exceeds 50%? Explain your answer.(D) If you were to use a 1% significance level, would the conclusion from Question 82change? Explain your answer.

Q: NARRBEGIN: SA_77_79The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization's staff of salespersons. He believes that the proportion of women in similar sales positions across the country in 2004 is less than 45%. Hoping to find support for his belief, he directs his assistant to collect a random sample of salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women.NARREND(A) State the appropriate null and alternative hypotheses in this situation.(B) Test this CEO's belief at the =.05 significance level and report the p-value. Do you find statistical support for his hypothesis that the proportion of women in similar sales positions across the country is less than 40%?(C) Suppose the sample size above is 100, instead of 50, and the sample proportion is again 0.36. Would this change your results in (B)? Explain your answer.

Q: NARRBEGIN: SA_72_76The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498.NARREND(A) Specify a hypothesis test to test the foundation's claim(B) Compared to the most recent survey, is this sample evidence statistically significant at the 10% level?(C) Compared to the most recent survey, is this sample evidence statistically significant at the 5% level?(D) Report and interpret the p-value for this test(E) Interpret the overall test for the foundation.

Q: NARRBEGIN: SA_70_71A study is performed in San Antonio to determine whether the average weekly grocery bill per five-person family in the town is significantly different from the national average. A random sample of 50 five-person families in San Antonio showed a mean of $133.474 and a standard deviation of $11.193.NARREND(A) Assume that the national average weekly grocery bill for a five-person family is $131. Is the sample evidence statistically significant? If so, at what significance levels can you reject the null hypothesis?(B) For which values of the sample mean (i.e., average weekly grocery bill) would you decide to reject the null hypothesis at the significance level? For which values of the sample mean would you decide to reject the null hypothesis at the 10% level of significance?

Q: NARRBEGIN: SA_66_69Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below.Test of 1500 versus one-tailed alternativeHypothesized mean1500Sample mean1509.5Std error of mean4.854Degrees of freedom24t-test statistic1.953p-value0.031NARREND(A) Can the sample size be determined from the information above? Yes or no? If yes, what is the sample size in this case?(B) The firm believes that the mean life is actually greater than 1500 hours, should you conduct a one-tailed or a two-tailed hypothesis test? Explain your answer, and state the appropriate null and alternative hypotheses.(C) What is the sample mean of this data? If you use a 5% significance level, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer.(D) If you were to use a 1% significance level in this case, would you conclude that the mean life of the light bulbs is typically more than 1500 hours? Explain your answer.