25 statistic questions - (23 of them are multiple choices )

Midterm Exam BA 376 Form #1 1. A hypothesis test returns a p-value of 0.04 against the null hypothesis that high school GPA and SAT scores amongst applicants to a college are independent. Which of the following is a correct interpretation of that p-value?

a) There is a 96% chance that the GPA and SAT scores are independent b) 4% of applicant's GPAs are independent from their SAT scores c) If SAT scores and GPA are independent, this extreme a result would happen 4% of the time d) We are 96% confident that GPA and SAT scores are independent. e) None of these is a correct intepretation of the p value. 2. A survey firm would like to determine whether the proportion of men who prefer to purchase clothing online is equal to the proportion of women who prefer to purchase clothing online.

Which test statistic would be most appropriate to use in this hypothesis test?

a) χτ2=∑ i∑ j (fij−eij)2 eij :χτ2≥χα,(rows −1)(col−1) b) χτ2=∑i=1 k (fi−ei)2 ei :χτ2≥χα,(rows −1) c) z= (̄p1− ̄p2)−(p1− p2) √̄p(1− ̄p)(1 n1 + 1 n2 ) d) z= (̄x1− ̄x2)−(μ1−μ2) √(σ12 n1 + σ22 n2 ) e) t= (̄x1− ̄x2)−(μ1−μ2) √(s12 n1 + s22 n2 ) 3. A credit scoring agency would like to test the hypothesis that region of residence (East, West, Midwest, South) is unrelated to (independent of) the likelihood of an approved borrower to default on an auto loan. Which test statistic would be most appropriate to use in this hypothesis test?

a) χτ2=∑ i∑ j (fij−eij)2 eij :χτ2≥ χα,(rows −1)(col−1) b) χτ2=∑i=1 k (fi−ei)2 ei :χτ2≥χα,(rows −1) c) z= (̄p1− ̄p2)−(p1− p2) √̄p(1− ̄p)(1 n1 + 1 n2 ) d) z= (̄x1− ̄x2)−(μ1−μ2) √(σ12 n1 + σ22 n2 ) e) t= (̄x1− ̄x2)−(μ1−μ2) √(s12 n1 + s22 n2 ) 4. The Nielsen Company reports what percentages of the television viewing public is watching each of the major networks on a Friday evening. Which test statistic would be most appropriate to test this hypothesis?

a) χτ2=∑ i∑ j (fij−eij)2 eij :χτ2≥χα,(rows −1)(col−1) b) χτ2=∑i=1 k (fi−ei)2 ei :χτ2≥χα,(rows −1) c) z= (̄p1− ̄p2)−(p1− p2) √̄p(1− ̄p)(1 n1 + 1 n2 ) d) z= (̄x1− ̄x2)−(μ1−μ2) √(σ12 n1 + σ22 n2 ) e) t= (̄x1− ̄x2)−(μ1−μ2) √(s12 n1 + s22 n2 ) 5. A call center wants to know whether the average call time for two groups of customers is different. The populaiton standard deviation is unkown. Which test statistic would be most appropriate to use in this hypothesis test?

a) χτ2=∑ i∑ j (fij−eij)2 eij :χτ2≥χα,(rows −1)(col−1) b) χτ2=∑i=1 k (fi−ei)2 ei :χτ2≥χα,(rows −1) c) z= (̄p1− ̄p2)−(p1− p2) √̄p(1− ̄p)(1 n1 + 1 n2 ) d) z= (̄x1− ̄x2)−(μ1−μ2) √(σ12 n1 + σ22 n2 ) e) t= (̄x1− ̄x2)−(μ1−μ2) √(s12 n1 + s22 n2 ) 6. A union wants to demonstrate that the average time to complete a building project with union carpenters is shorter than the average time to complete a building project without union carpenters. The two population standard deviations are assumed to be known. Which test statistic would be most appropriate to use in this hypothesis test?

a) χτ2=∑ i∑ j (fij−eij)2 eij :χτ2≥χα,(rows −1)(col−1) b) χτ2=∑i=1 k (fi−ei)2 ei :χτ2≥χα,(rows −1) c) z= (̄p1− ̄p2)−(p1− p2) √̄p(1− ̄p)(1 n1 + 1 n2 ) d) z= (̄x1− ̄x2)−(μ1−μ2) √(σ12 n1 + σ22 n2 ) e) t= (̄x1− ̄x2)−(μ1−μ2) √(s12 n1 + s22 n2 ) 7. When calculating the critical value for a t distribution to test the difference of two means, the equation for determining the degrees of freedom is fairly complex. What is the effect of using the smaller of the two sample sizes rather than that equation?

a) The confidence interval is narrower because the degrees of freedom will be smaller. b) The confidence interval is wider because the degrees of freedom will be smaller. c) The confidence interval is narrower because the degrees of freedom will be greater. d) The confidence interval is wider because the degrees of freedom will be greater. e) None of the above 8. A 90% confidence interval for the difference between two proportions is {-.02 to .35}. What is the result of a test at 95% confidence of the null hypothesis that there is no difference between the two proportions?

a) Reject the null hypothesis for this data at the given level of significance b) Fail to reject the null hypothesis for this data at the given level of significance c) This problem cannot be answered because the two levels of confidence are different d) This problem cannot be answered because there is no relationship between confidence intervals and hypothesis tests. e) None of the above 9. A study by the Pew Research Center for the People & the Press showed that in the period from 2010 to 2012, US residents were much less likely to rate the New York Times as “trustworthy”:

in 2010 56% rated the New York Times as trustworthy, while in 2012 only 49% were rated as trustworthy. Assume the 2010 numbers were based on 250 respondents and the 2012 numbers were based on 300 respondents. What is the appropriate test statistic for the hypothesis that there has been no change in US residents' perception of the trustworthiness of the New York Times?

a) z= (.49 −.56 )−0.07 √.56 (1−.56 )( 1 250 + 1 300 ) b) z= (.49 −.56 )−0 √.56 (1−.56 )( 1 250 + 1 300 ) c) z= (.49 −.56 )−0.07 √ 287 550 (1− 287 550 )( 1 250 + 1 300 ) d) z= (.49 −.56 )−0 √ 287 550 (1− 287 550 )( 1 250 + 1 300 ) e) none of the above. 10. A study by the Pew Research Center for the People & the Press showed that in the period from 2010 to 2012, US residents were much less likely to rate the New York Times as “trustworthy”:

in 2010 56% rated the New York Times as trustworthy, while in 2012 only 49% were rated as trustworthy. Assume the 2010 numbers were based on 250 respondents and the 2012 numbers were based on 300 respondents. What is the result of the test of the hypothesis ( α= 0.05) that there has been no change in US residents' perception of the trustworthiness of the New York Times?

a) Because the p-value is large enough, we reject the null hypothesis b) Because the p-value is small enough, we reject the null hypothesis c) Because the p-value is too large, we cannot reject the null hypothesis d) Because the p-value is too small, we cannot reject the null hypothesis e) None of the above 11. The hypothesis test in the previous two questions was two-tailed. In what way is a two-tailed hypothesis test different than a one-tailed test?

a) An efffect can only be detected in one direction, and the p-value is halved. b) An efffect can only be detected in one direction, and the p-value is doubled. c) An efffect in either direction can be detected, and the p-value is halved. d) An efffect in either direction can be detected, and the p-value is doubled. e) none of the above To answer the next two questions, consider the table below, which shows a random sample of six textbooks used in OSU courses: Textbook OSU Bookstore Price Amazon Price Difference Financial Accounting 100.13 68.99 31.14 International Business 239.18 209.47 29.71 Legal Environment of Business 282.38 198.85 83.53 Principles of Marketing 81.90 33.99 47.91 Financial & Managerial Accounting for MBAs 139.50 193.98 -54.48 Marketing Management 222.08 108.98 113.10 12. What is the appropriate test statistic to use the table above to test the hypothesis that OSU bookstore is no more expensive than Amazon? ? a) t= 1.789 b) χ2=1.789 c) t=253.56 d) χ2= 253.56 e) none of these 13. What is the appropriate critical value for a hypothesis test with α = 0.05 against the null hypothesis that OSU bookstore is no more expensive than Amazon?

a) tc=1.943 b) χc2=12.832 c) χc2= 2.571 d) tc= 2.015 e) none of these For questions 14-18, consider the table below which shows the actual and expected proportion of customers who prefer certain types of spaghetti sauce (H 0: p1=p 2=p 3=p 4): Type Expected (e i) Actual (f i) Difference (f i-ei) (fi-ei)2/ei Hot 10 7 -3 .9 Medium 9 -1 .1 Mild 10 8 -2 Extra Chunky 10 6 3.6 Total 40 40 14. How many customers were expected to prefer Medium spaghetti sauce? How many actually favored Extra Chunky?

a) 0 expected for Medium, 16 actual for extra chunky b) 10 expected for Medium, 16 actual for extra chunky c) 0 expected for Medium, 4 actual for extra chunky d) 10 expected for Medium, 4 actual for extra chunky e) none of the above 15. Use the table to calculate the value of the test statistic.

a) χ2= 4.6 b) χ2= 5 c) χ2=0 d) χ2=3.6 e) none of these 16. How many degrees of freedom for this chi-squared distribution?

a) 3 b) 4 c) 9 d)12 e) none of these 17. What is the critical value for the hypothesis test at 90% confidence?

a) χc2= 6.251 b) χc2=0.584 c) χc2=7.779 d) χc2=1.064 e) none of these 18. What is an appropriate statistical conclusion for this hypothesis test at 90% confidence?

a) Because the test statistic exceeds the critical value, we fail to reject the null hypothesis b) Because the test statistic exceeds the critical value, we reject the null hypothesis c) Because the test statistic does not exceed the critical value, we fail to reject the null hypothesis d) Because the test statistic does not exceed the critical value, we reject the null hypothesis e) none of these For questions 19-21, researchers want to know whether a customer chooses to purchase an extended warranty depends upon the age of the customer. The data the researchers find is in the table: Age Group Purchased Warranty Declined Warranty Total 18-30 6 15 21 31-40 10 20 30 41-50 10 9 19 51-60 9 11 20 61+ 15 20 35 Total 50 75 125 19. How do we calculate the table of expected values, assuming age group and likelihood of purchasing warranty are independent? Based on the table below, calculate the expected number of 41-50 year olds who will purchase a warranty, assuming independence.

a) 8.4 b) 8 c) 9 d)10 e) 7.6 Expected values Age Group Purchased Warranty Declined Warranty Total 18-30 21 31-40 30 41-50 19 51-60 20 61+ 35 Total 50 75 125 20. When calculating the chi-squared statistic, what contribution is made by the difference in the number of 31-40 year olds who Decline Warranty compared to the expectation under the null?

a) 0.04 b) -2 c) 0.2 d)18 e) none of these 21. Which of the following is a reasonable explanation for why the age groups are not evenly divided by decade (in other words, why were some age groups combined?

a) The chi-squared test can have a maximum of 5 rows. b) Each cell in the expected table must have a count of at least 5 to use this test c) The fact that the age groups are not evenly divided by decade is an error which invalidates the test d) Each cell in the actual data must have a count of at least three in each cell to use this test. e) None of these is a possible explanation. 22. Given the following information, calculate a 95% confidence interval for the difference between the two population means μ1 and μ 2: ̄x1=9 ̄x2=12 σ1=3 σ2=2 n1= 20 n2=10 a) −3±1.645 √ 3 20 + 2 10 b) −3±1.96 √ 3 20 + 2 10 c) −3±1.645 √ 9 20 + 4 10 d) −3± 1.96 √ 9 20 + 4 10 e) none of these 23. When would we use a t distribution to find the difference between two means?

a) When s 1 and s 2 are unknown b) When s 1 and s 2 are known c) When σ1 and σ2 are unknown d) When σ1 and σ2 are known e) none of these. 24. A statgraphics program returns the following output for a test of independence of two categorical variables (gender and highest degree completed) : Test Statistic Df P-Valu Chi-Square 12.881 2 0.0016 What does the p-value of 0.0016 mean in this case? Be as specific as you can. You may use diagrams to illustrate your point if necessary. (4 pts) If gender and highest degree completed are really indepndent of one another, there is very little chance (0.16%) of getting such a close relationship in our data by random chance. 25. Decribe the differnce between finding the difference between two populatio means with independent samples vs. matched samples. (1 pt) Give an example of each. (2 pts) How can you tell which one is appropriate in a given situation? (1 pt) Using matched samples can lead to higher certainty and narrower confidence intervals/ more power than considering the same data as if it were from independent samples. When each subject is measured twice (two different values for each individual), then it is appropriate to use the matched sample technique. For instance, if we weigh a group of dieters and non-dieters we would consider these independent samples, whereas if we measured people before and after a diet these would be considered matched samples. 26. Bonus: I'm interested in any feedback you're willing to give about how this class is going for you so far. For one point each (optional, extra credit) plese tell me:

a) What is one thing that has supported your learning in BA 376 so far this term? b) What is one thing you could do better to get more out of this class? c) What is one thing I could do better to help you get more out of this class? Thank you!