BA 253: Take Home Exam 3
Due on Friday 11/13/15 by 3:15pm.
For this Take Home Exam, you may work in groups of up to three students, as long as all group members put in an equal amount of effort. No freeloaders! I will likely curve the final average so giving away answers is not in your best interest (and it’s cheating). However, feel free to work together and compare your answers with other groups in the interest of truly understanding the material. I strongly suggest that you do the problems individually, compare them, and then write down your best answer.
For each hypothesis test, show your work: Set up the null and alternative hypotheses, determine your answer and write your final answer in a short sentence. On some problems I will ask you to determine your answer via the critical value(s) and test statistic, on others via the p-value and significance level – follow the instructions. Similarly, on some problems I will provide the data and on others you will need to refer to the “Fake Data” MS Excel file available online. You may do your work by hand or with the aid of the TI calculator or MS Excel, but show/explain your work for each problem. Be sure to answer every part of every question.
Good Luck!
Names:______
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1) (4 points)Assume that nationally, on average, it takes college students 4.3 years to graduate. How long does it take at FLC? You survey 46 recent FLCgraduates and find that their average was 4.8 years with standard deviation 0.8 years. At α = 3%, do FLC students take significantly longer to graduate than the national average?Solve by comparing the test statistic to the critical value(s). How compelling is your result?
2) (4 points)According to the bottle, A1 Steak Sauce is “served in 9 out of 10 steakhouses.” Is this true? Assume that you randomly visit n = 60 steakhouses and find that A1 is served in x = 52 of them. a) Calculate the sample proportion p. Just by looking at it, does it seem low enough to refute the claim on the bottle? b)At α = 5%, is the true population proportion really 9/10 or is it actually lower? Answer using the p-value. c)Interpret the p-value – is the claim on the bottle confirmed, plausible or busted? d)How small would x need to be in order to reject H0?
Exam 1 / Exam 2 / Exam 3
75 / 78 / 55
78 / 75 / 50
67 / 95 / 96
68 / 72 / 27
74 / 100 / 69
60 / 75 / 30
88 / 78 / 18
70 / 92 / 52
94 / 81 / 58
82 / 73 / 63
3) (4 points) A professor has just graded three different versions of an exam, with the data in the table on the right. Are the three versions fair (i.e., do they have similar averages) or are they unfair (i.e., do they have different averages)?
a)Calculate the sample mean and standard deviation for each exam. Just by looking at the statistics, do the three versions seem fair?
b)Use ANOVA at α = 5% to determine the population meansare the same or different. Are the different versions of the exams fair or unfair?
c) Interpret the p-value.
d) Which version of the exam would you prefer to take?
4) (3 points)For this question, refer to the Fake Data spreadsheet. At α = 5%, is the average response for men for Question 4 significantly smaller than the average response for women for Question 4? a) Sort the data appropriately and determine the average and standard deviation for both genders. b) Solve using a two sample t-test (assuming “Yes” for Pooled) by looking at the p-value.
5) (4 points) For this question, refer to the Fake Data spreadsheet. a) Find a 95% confidence interval for the Question 6 responses, b) listing the appropriate t-value. c) At α = 5%, test whether the true population mean for this question is 42 or something different, d) by comparing the test statistic to the critical value(s).
6) (4 points)For this question, refer to the Fake Data spreadsheet. At α = 5%, are the proportions of “Yes” answers for Question 2 and Question 3 the same or different? a) Calculate the sample proportion of “Yes” answers for the responses to Question 2 and to Question 3 – do they appear similar or different? b) Test the hypothesis using the p-value.c) According to the p-value, how compelling are the results?