25 statistic questions, writing homework help

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I have 25 question (23 of them are multiple choices questions)

I have two old solved assignments that can help you.

I need to get full mark if you can do it please do not paid

1. A hypothesis test returns a p-value of 0.04 against the null hypothesis: First graders in 2016 were evenly split between favoring puppies, kittens, and unicorns. What is a correct interpretation of this p-value? a. Only 4% of first graders were not evenly split between these categories. b. If the first graders were evenly split between these categories, there is only a 4% chance of getting such an extreme result. c. Only 4% of first graders were evenly split between these categories. d. If the first graders really were not evenly split between these categories, there is only a 4% chance of getting such an extreme result. e. None of these is a correct interpretation of the p-value. 2. For the same set of first graders, a researcher would like to know whether there is a difference in the proportion that prefer puppies versus the proportion that prefer kittens. Which test statistic would be most appropriate to use in this hypothesis test? 3. For the same set of first graders, a researcher was wanting to check whether the students’ likelihood of eating glue (yes, they have tried it/no, it’s not food) depended on which animal they favored. Which test statistic would be most appropriate to use in this hypothesis test? 4. A researcher would like to know if first graders were evenly split between favoring puppies, kittens, or unicorns. Which test statistic would be most appropriate to use in this hypothesis test? 5. A researcher was interested in comparing reading speeds (in words per minute) between first graders that prefer kittens versus first graders that prefer unicorns. Because this is a new area of research, we do not have a value for either population standard deviation. Which test statistic would be most appropriate to use in this hypothesis test? 6. A researcher was interested in comparing heights between first graders that prefer puppies to first graders that prefer kittens. The researcher is willing to assume that the population standard deviation for each of these populations is known. Which test statistic would be most appropriate to use in this hypothesis test? 7. Would it be appropriate to use the equation 𝑑 = 𝑑̅ βˆ’π·0 to test the difference in #6 𝑠𝑑 β„βˆšπ‘› above? a) Yes because this is matched (paired) data. b) Yes because this is not matched data. c) No because this is matched (paired) data. d) No because this is not matched data. e) None of the above. 8. Facebook recently estimated that 5.1% to 11.2% of its accounts were fake. Assuming this is a 95% confidence interval, what does it say about a test of the null hypothesis: 5% of Facebook Accounts are fake tested at 95% confidence? 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 identical d) This problem cannot be answered because there is no relationship between confidence intervals and hypothesis tests. Use the following for questions 9 through 11: A study by the Robert Morris polling institute found that 44% of former football players (at any level) supported banning tackle football prior to middle school while 46% of parents supported such a ban. For the questions that follow, assume this survey was based on two independent samples, one of 350 former players and one of 650 parents of players. 9. What is the appropriate null and alternative hypothesis to check whether there was a statistically significant difference between these two percentages? a) 𝐻0 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  ≀ π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  , 𝐻𝐴 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  > π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  b) 𝐻0 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  < π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  , 𝐻𝐴 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  β‰₯ π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  c) 𝐻0 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  = π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  , 𝐻𝐴 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  β‰  π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  d) 𝐻0 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  β‰₯ π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  , 𝐻𝐴 : π‘π‘“π‘œπ‘Ÿπ‘šπ‘’π‘Ÿ π‘π‘™π‘Žπ‘¦π‘’π‘Ÿπ‘  < π‘π‘π‘Žπ‘Ÿπ‘’π‘›π‘‘π‘  10. What is the appropriate test statistic to use for the above test? 11. What is the result of the test of the null hypothesis (𝛼 = 0.05) that former football players and parents of football players are equally likely to support this ban?
1. A hypothesis test returns a p-value of 0.06 against the null hypothesis: The identification of an elementary student as"gifted" is independent of their identification as dyslexic. What is a correct interpretation of this p-value? a) Only 6% of dyslexic students are identified as "gifted". b) Elementary students with dyslexia are only identified as "gifted" 96% as often as their nondyslexic peers. c) There is a 94% chance that dyslexia is independent from whether an elementary student is identified as "gifted". d) If dyslexia is independent from whether an elementary student is identified as "gifted", we would get a result indicating at least this much connection between the two 6% of the time. e) None of these is a correct interpretation of the p value. 2. A sales manager would like to know whether the male or female employees at her company are more likely to have a larger average number of sales. The manager does not know either population standard deviation. Which test statistic would be most appropriate to use in this hypothesis test? k ( f ijβˆ’e ij ) 2 2 ( f iβˆ’e i )2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 d) z= 1 2 e) t= 1 2 x 2 2 2 2 1 1 Οƒ Οƒ s s Μ„p (1βˆ’ Μ„p )( + ) ( 1+ 2) ( 1+ 2) n1 n 2 n1 n2 n1 n2 √ √ √ 3. A school district equity officer wants to test the null hypothesis that dyslexia is independent of whether an elementary student is identified as "gifted". Which test statistic would be most appropriate to use in the hypothesis test? k ( f ijβˆ’e ij ) 2 2 ( f iβˆ’e i )2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) X :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 d) z= 1 2 e) t= 1 2 2 2 2 2 1 1 Οƒ1 Οƒ2 s1 s 2 Μ„p (1βˆ’ Μ„p )( + ) ( + ) ( + ) n1 n 2 n n n n √ √ 1 2 √ 1 2 4. A politician wants to know whether the level of support for a certain ballot initiative is higher among Republicans than Democrats. Which test statistic would be most appropriate to test this hypothesis? k ( f ijβˆ’e ij ) 2 2 ( f iβˆ’e i )2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 X d) z= 1 2 e) t= 1 2 1 1 Οƒ 21 Οƒ 22 s12 s 22 Μ„p (1βˆ’ Μ„p )( + ) ( + ) ( + ) n1 n 2 n1 n2 n 1 n2 √ √ √ 5. An amusement park believes that 25% of attendants are under 12 years old, 20% are between 12 and 16 years old, 15% are between 16 and 24 years old, and 40% are over 24 years old. Which test statistic would be most appropriate to use in this hypothesis test? k ( f ijβˆ’e ij ) 2 2 ( f iβˆ’e i )2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) X a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 d) z= 1 2 e) t= 1 2 2 2 1 1 Οƒ1 Οƒ2 s12 s 22 Μ„p (1βˆ’ Μ„p )( + ) ( + ) ( + ) n1 n 2 n1 n2 n1 n2 √ √ √ 6. An electronics company wants to demonstrate that its devices have longer average battery life than the next closest competitor. The two population standard deviations are assumed to be known. Which test statistic would be most appropriate to use in this hypothesis test? 2 2 k ( f ijβˆ’e ij ) ( f iβˆ’e i ) 2 2 2 :Ο‡ 2Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) c) z= 1 d) t= 1 2 e) z= 1 2 X 2 2 2 2 1 1 s s Οƒ Οƒ Μ„p (1βˆ’ Μ„p )( + ) ( 1+ 2) ( 1+ 2) n1 n 2 n1 n2 n1 n2 √ √ √ sd to estimate the difference between means? √n When each element of the sample is measured twice (for instance "before" and "after" data) When the two underlying populations are not normally distributed. When the two standard deviations are identical When the two standard deviations are unknown None of the above 7. When is it appropriate to use the equation dΜ„ Β±t a) b) c) d) e) 8. A 95% confidence interval for the difference between two proportions is {.02 to .35}. What is the result of a test at 90% confidence of the null hypothesis: 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 Use the following for questions 9 through 11: A study by the Pew Research Center for The People & The Press showed that in July 2013, a minority of American adults approved of the NSA's surveillance programs. However, when the question's wording mentioned that this surveillance happened with court approval, substantially more people (37% instead of 25%) approved of the program. 9. What is the appropriate test statistic to check whether there was a statistically significant difference between these two percentages, assuming there were 1000 people questioned in each group? (.37βˆ’.25)βˆ’0 a) z= X 1 1 .31(1βˆ’.31)( + ) 1000 1000 (.37βˆ’.25)βˆ’0 b) z= 1 1 .37(1βˆ’.37)( + ) 1000 1000 (.37βˆ’.25)βˆ’0 c) z= 1 1 .37(1βˆ’.25)( + ) 1000 1000 (.37βˆ’.25)βˆ’0 d) z= 1 1 .25(1βˆ’.25)( + ) 1000 1000 e) none of the above. √ √ √ √ 10. What is the result of the test of the null hypothesis (Ξ±= 0.05) that mentioning court approval has no effect on answers to this survey? 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. Is it appropriate to test this question using a one-tailed or a two-tailed test? a) One tailed because mentioning court approval could only possibly affect people's answers in one direction. b) Two tailed because it's possible that mentioning court approval could affect people's answers in either direction. c) One tailed because it's possible that mentioning court approval could affect people's answers in either direction. d) Two tailed because mentioning court approval could only possibly affect people's answers in one direction. e) none of the above For question 12 and 13: The Gallup organization is interested in whether the Affordable Care Act's ("Obamacare's") support may be changing. In August, Gallup reported that among registered voters in the United States, 41% approved, 49% disapproved, and 11% had no opinion (the percents do not add to 100% due to rounding error). In October, Gallup surveyed 1528 registered voters: 679 approved, 762 disapproved, and 87 had no opinion. Is there evidence that voters' opinions have changed between August and October? 12. What is the appropriate test statistic to test the null hypothesis- opinions have NOT changed between August and October? t=43.75 a) b) Ο‡ 2=43.75 X c) t=0.027 d) Ο‡ 2=0.027 13. What is the appropriate critical value for the hypothesis test above at 95% confidence? a) 5.991 b) 7.378 c) 7.815 d) 9.348 e) none of these For questions 14-18, consider the table below with opinions about the Affordable Care Act broken down by age categories. 18 to 29 30 to 49 50 to 64 65+ Total Approve 76 92 72 29 269 Disapprove 66 94 94 40 294 No Opinion 8 12 9 6 35 Total 150 200 175 75 600 14. How many 18-29 year-olds in this survey would be expected to disapprove of the Affordable Care Act if age and opinion were independent? a) b) c) d) e) (66/150)*(66/294) = 0.098 (150/600)*(294/600)*600 = 73.5 66 (66/150)*(66/294)*600 = 59.27 None of the above 15. Can we use our chi-squared test for this data? a) b) c) d) note that our "expected value" No, because we expect a value of at least five in each box. in one box is 4.375, calling th No, because we expect a value of less than five in some boxes. Yes, because we expect a value of at least 5 in each box chi-squared approach into quest Yes, because we expect a value of less than five in some boxes. 16. Assuming we can use the chi-squared distribution for this test, how many degrees of freedom would we have? a) 3 b) 4 c) 6 d)12 e) none of these 17. If one of our assumptions is not met, which of the following is an option to still use the chisquared distribution? a) Decrease the degrees of freedom for our chi-square statistic. b) Separate columns or rows so that each box has an expected count less than five. c) Use a z distribution instead d) Combine columns or rows so that each box has at an expected count of at least five. 18. If we can perform a chi-squared distribution and we get a p-value of 0.002, what is an appropriate statistical interpretation of that p-value? a) Assuming the null hypothesis is correct, there is only a 0.2% chance of getting a result this extreme. Such a low p-value is generally considered good evidence to reject the null. b) Assuming the alternative hypothesis is correct, there is only a 0.2% chance of getting a result this extreme. Such a low p-value is generally considered good evidence to reject the null. c) Assuming the null hypothesis is correct, there is only a 0.2% chance of getting a result this extreme. Such a large p-value is generally not generally considered enough evidence to reject the null. d) Assuming the alternative hypothesis is correct, there is only a 0.2% chance of getting a result this extreme. Such a large p-value is generally not generally considered enough evidence to reject the null. e) none of these 19. Given the following information, calculate a 95% confidence interval for the difference between the two population means ΞΌ1 and ΞΌ2: s12=5 s 22=4 n1=17 n2 =15 4 5 5 4 b) βˆ’2Β±2.145 X βˆ’2Β±2.145 + + 17 15 17 15 xΜ„1=6 a) xΜ„2=8 √ √ c) βˆ’2Β±1.96 5 4 + 17 15 d) βˆ’2Β±1.96 √ √ 4 5 + 17 15 For questions 20-23, a company is interested in whether customer satisfaction depends on the sales region by which they are served. The following table summarizes the data found by the researchers: Region Highly Satisfied Somewhat Satisfied Somewhat Dissatisfied Highly Dissatisfied Total Western 90 46 8 6 150 Southern 10 40 42 8 100 Midwestern 117 94 75 14 300 Eastern 171 144 65 20 400 26 10 2 50 Alaska & Hawaii 12 Total 400 350 200 50 1000 20. How do we calculate the table of expected values, assuming region and satisfaction are independent? Based on the table below, calculate the expected number of customers in the Western region who will be highly satisfied, assuming independence. a) 60 Region b) 30 Highly Satisfied c) 900 Somewhat Satisfied d)90 e) none of these Somewhat Dissatisfied Highly Dissatisfied Total Western 150 Southern 100 Midwestern 300 Eastern 400 Alaska & Hawaii 50 Total 400 350 200 50 1000 21. When calculating the chi-squared statistic, what contribution is made by the difference in the number of Alaskan or Hawaiian customers who are Somewhat Dissatisfied compared to the expectation under the null? a) 12.1 b) 10 c) 100 d)0 e) none of these 22. Unfortunately, this data cannot be tested using the chi-squared test statistic. Why? a) The expected count in the bottom right box (Alaska & Hawaii highly dissatisfied) is too large. b) The expected count in the bottom right box (Alaska & Hawaii highly dissatisfied) is too small. c) The actual count in the bottom right box (Alaska & Hawaii highly dissatisfied) is too small. d) The actual count in the bottom right box (Alaska & Hawaii highly dissatisfied) is too large. e) None of these is a possible explanation. 23. What could be done to use the test after all? a) Combine Alaska and Hawaii with another row (for instance Western Region) b) Combine "Highly Dissatisfied" with another column (for instance Somewhat Dissatisfied) c) Either (a) or (b) would work, although they might result in different p-values and interpretations. d) Either (a) or (b) would work, and they would result in identical p-values and interpretations 24. A statgraphics program returns the following output for a test of goodness of fit against the null hypothesis - participants at a conference are evenly distributed across several responses to the question "Which of the following was your strongest reason for attending the conference?": Test Chi-Square Statistic 12.873 Df 7 P-Value ????????? a) How many responses were there to the question in the study? (1 point) 8 (degrees if freedom = category -1) b) Give an estimate for the p-value of this test. (1 point) between 5% and 10% c) What does this tell you about the participants at the conference and t heir reasons for attending?(2 points) Not all reasons for attending were equally likely to be selected. (assuming alpha = 0.10; if alpha = 0.05 then we couldn't conclude anything) 25. A company wants to know whether their automotive fleet gets better gas economy (in terms of miles per dollar) with regular or supreme gasoline. a) Would you test this using a paired or unpaired t test? (1 point) answers will vary b) Why would you recommend this type of test?(3 points) advantages to paired test: decrease number of cars needed, lower variability because don't have to worry about variability between types of car advantages to unpaired test: don't need to worry about order effects 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) please 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!
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? k ( f ijβˆ’e ij ) 2 2 ( f iβˆ’e i )2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p 1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 d) z= 1 2 e) t= 1 2 1 1 Οƒ 21 Οƒ 22 s12 s 22 Μ„p (1βˆ’ Μ„p ) ( + ) ( + ) ( + ) n1 n 2 n n n n √ √ 1 2 √ 1 2 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? k ( f ij βˆ’e ij )2 2 ( f iβˆ’e i )2 2 2 2 : Ο‡ Ο„β‰₯χα ,(rowsβˆ’1)(col βˆ’1) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ e ij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 d) z= 1 2 e) t= 1 2 2 2 2 2 1 1 Οƒ1 Οƒ2 s1 s 2 Μ„p (1βˆ’ Μ„p )( + ) ( + ) ( + ) n1 n 2 n n n n √ √ 1 2 √ 1 2 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? k ( f ijβˆ’e ij ) 2 2 ( f iβˆ’e i )2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) : Ο‡ Ο„ β‰₯Ο‡ Ξ± ,(rowsβˆ’1 ) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 d) z= 1 2 e) t= 1 2 1 1 Οƒ 21 Οƒ 22 s12 s 22 Μ„p (1βˆ’ Μ„p )( + ) ( + ) ( + ) n1 n 2 n1 n2 n1 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? k ( f ijβˆ’e ij ) 2 2 ( f iβˆ’e i )2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) c) z= 1 d) z= 1 2 e) t= 1 2 2 2 1 1 Οƒ1 Οƒ2 s 21 s 22 Μ„p (1βˆ’ Μ„p )( + ) ( + ) ( + ) n1 n 2 n1 n2 n1 n 2 √ √ √ 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? 2 2 k ( f ijβˆ’e ij ) ( f iβˆ’e i ) 2 2 2 2 :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1)(col βˆ’1 ) :Ο‡ Ο„ β‰₯χα ,(rowsβˆ’1) a) Ο‡ Ο„ =βˆ‘i βˆ‘ j b) Ο‡ Ο„ =βˆ‘ eij ei i=1 ( pΜ„ βˆ’ pΜ„2)βˆ’( p1βˆ’ p2 ) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ 1βˆ’ΞΌ 2) ( xΜ„ βˆ’ xΜ„ )βˆ’(ΞΌ1βˆ’ΞΌ 2 ) c) z= 1 d) z= 1 2 e) t= 1 2 2 2 2 2 1 1 Οƒ1 Οƒ 2 s1 s 2 Μ„p (1βˆ’ Μ„p )( + ) ( + ) ( + ) n1 n 2 n1 n 2 n 1 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 β€œtrustworthy”: 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? (.49βˆ’.56)βˆ’0.07 a) z= 1 1 .56(1βˆ’.56)( + ) 250 300 ( .49βˆ’.56)βˆ’0 b) z= 1 1 .56(1βˆ’.56)( + ) 250 300 (.49βˆ’.56)βˆ’0.07 c) z= 287 287 1 1 (1βˆ’ )( + ) 550 550 250 300 (.49βˆ’.56)βˆ’0 d) z= 287 287 1 1 (1βˆ’ )( + ) 550 550 250 300 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 β€œtrustworthy”: 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 (Ξ±= 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 139.50 Accounting for MBAs 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) Ο‡ 2=1.789 c) t=253.56 d) Ο‡ 2=253.56 e) none of these 13. What is the appropriate critical value for a hypothesis test with Ξ± = 0.05 against the null hypothesis that OSU bookstore is no more expensive than Amazon? a) t c =1.943 b) Ο‡ 2c =12.832 c) Ο‡ 2c =2.571 d) t c =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=p2=p3=p4): Type Expected (ei) Actual (fi) Difference (fi-ei) (fi-ei)2/ei Hot 10 7 -3 .9 9 -1 .1 8 -2 Medium Mild 10 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) Ο‡ 2=4.6 b) Ο‡ 2=5 c) Ο‡ 2=0 d) Ο‡ 2=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) Ο‡ 2c =6.251 b) Ο‡ 2c =0.584 c) Ο‡ 2c =7.779 d) Ο‡ 2c =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 ΞΌ1 and ΞΌ2: xΜ„1=9 a) xΜ„2=12 βˆ’3Β±1.645 Οƒ 1=3 √ Οƒ 2=2 3 2 + 20 10 c) βˆ’3Β±1.645 √ 9 4 + 20 10 n1=20 n 2=10 √ √ b) βˆ’3Β±1.96 d) βˆ’3Β±1.96 3 2 + 20 10 9 4 + 20 10 e) none of these 23. When would we use a t distribution to find the difference between two means? a) When s1 and s2 are unknown c) When Οƒ1 and Οƒ2 are unknown e) none of these. b) When s1 and s2 are known d) When Οƒ1 and Οƒ2 are known 24. A statgraphics program returns the following output for a test of independence of two categorical variables (gender and highest degree completed) : Test Chi-Square Statistic 12.881 Df 2 P-Valu 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!

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