Exam 3 Practice Exam
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Muhlenberg College *
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119
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Mathematics
Date
Feb 20, 2024
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7
Uploaded by BrigadierStingrayPerson1009
Exam 3
MTH 119 Statistical Analysis Spring 2018 Name: _________________________________________ I will uphold the AIC of Muhlenberg College (sign here): _________________________________ Directions for exam:
Write clearly –
I cannot grade it if I cannot read it
Show all work to receive full credit. Problem Points Possible Points Received 1 12 2 Part 1 16 3 6 4 Part 1 8 4 Part 2 18 5 Part 1 11 5 Part 2 4 Total 75
Problem 1 (12 points total, 2 points each) For each scenario, circle the most appropriate parameter of interest. a.
Compare the average number of calories consumed at a typical Passover Seder to the average calories consumed during an Easter meal. Single Proportion Difference in Proportions Single Mean Difference in Means Matched Pairs Means b.
You’re curious if there is a larger proportion of athletes that stayed on campus over the long
-weekend than non-athletes. Single Proportion Difference in Proportions Single Mean Difference in Means Matched Pairs Means c.
Calculate the average number of Easter eggs kids found during an Easter egg hunt. Single Proportion Difference in Proportions Single Mean Difference in Means Matched Pairs Means d.
Estimate the proportion of people that like black jelly beans. Single Proportion Difference in Proportions Single Mean Difference in Means Matched Pairs Means e.
To see if students did more work over Spring break or Easter/Passover break, you ask each student how many hours of work they did over each break and calculate the difference for each student. Single Proportion Difference in Proportions Single Mean Difference in Means Matched Pairs Means f.
Compare the proportion of people that overate during Passover to the proportion of people that overate during Easter. Single Proportion Difference in Proportions Single Mean Difference in Means Matched Pairs Means
Problem 2 You want to know if the average age of US quarters in circulation is less than the average age of US nickels in circulation. (FYI: You suspect this may be true as quarters minted prior to 1965 contained silver and are worth far more than 25 cents, so people tend to take old quarters out of circulation, whereas nickels have remained largely unchanged si
nce the 1930’s.
)
a.
(4 points) State a null and alternative hypothesis to test the claim stated above. Ho: Ha: b.
(4 points) Suppose Dr. Davidson goes through Mackenzie’s piggy bank and calculates the average age of Mackenzie’s quarters to be 25.7 years and the average age of Mackenzie’s nickels to be 30.4 years. State the sample statistic you’d use to test the hypotheses and label with a well
-labeled symbol. c.
(3 points) Sketch the null distribution, labeled with the center value, sample statistic, and p-value (shading). d.
(2 points) Dr. Davidson finds that the p-value is 0.002. Using an alpha level of 0.05, would you reject Ho? Briefly explain. e.
(3 points) State your conclusions to the test in terms of the problem.
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Problem 3 (6 points) Dr. Davidson’s daughter, Mackenzie, is 37 inches tall. The average height for 2.5 year olds is 35 inches with a standard deviation of 1.46. Dr. Davidson’s unborn baby (“Baby Scott”), they estimate, weighs about 5.5 pounds. The average weight of a 32-week-old-fetus is 4.25 pounds with a stand
ard deviation of 1.28 pounds. Which child’s growth is “more extreme” for their age? Justify using mathematics, being sure to show all relevant work. Height information was taken from all.life (2018) and average weight information from Baby2see.com (2018). Problem 4 At the beginning of the semester, Dr. Davidson asked students their gender and the mode of social media they prefer. Below is a summary of the results from both sections she teaches combined. We will use the following data to estimate social media preferences of Muhlenberg College students in general. Facebook Instagram Twitter Total Female 4 21 5 30 Male 4 15 2 21 Total 8 36 7 51 a.
(3 points) What proportion of students prefer Instagram for social media? Calculate the value and label with an appropriate symbol. b.
(3 points) Dr. Davidson calculates the 95% confidence interval to be (0.56, 0.82). Interpret this interval in context of the problem. c.
(2 points) Do you have evidence that “most” (more than half) of students prefer using Instagram? Briefly explain.
Problem 4 Continued d.
(3 points) Calculate the proportion of females that prefer using Instagram and label with an appropriate symbol. e.
(3 points) Calculate the proportion of males that prefer using Instagram and label with an appropriate symbol. f.
(4 points) Suppose you want to know if there is a difference in the proportion of females that prefer Instagram and the proportion of males that prefer Instagram. State the null and alternative hypotheses you’d use in this situation in well-labeled symbol form. Ho: Ha: g.
(4 points) Calculate the sample statistic you’d use to test the hypothesis and label with a well
-labeled symbol. h.
(2 points) Dr. Davidson calculates a 95% confidence interval to be (-0.28, 0.25). Should you reject Ho? Briefly explain. i.
(2 points) Do we have evidence that males prefer Instagram more than females? Briefly explain. Facebook Instagram Twitter Total Female 4 21 5 30 Male 4 15 2 21 Total 8 36 7 51
Problem 5 The authors of your textbook took a sample of 970 movies and compared each movie’s rating between Rotten Tomatoes reviewers and a general audience. You speculate that reviewers will be more critical than a general audience and therefore a movies’ audience score will be higher than the Rotten Tomatoes reviewer score. Use the output exploring the difference in rating between audience score and review score (AudienceScore-RottenTomatoes). a.
(2 points) What type of test (of the 5 tests in Chapter 6) is appropriate to explore this data? Briefly explain. b.
(2 points) As described above, is this a one or two-sided test? Briefly explain. c.
(4 points) State appropriate null and alternative hypotheses (in symbol form). Ho: Ha: d.
(3 points) Referencing the output above, what does it mean for the difference in scores to be: Positive: Negative: Equal to 0:
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Problem 5 Continued e.
(2 points) Interpret the graph in terms of the problem. f.
(2 points) Specifying specific output used and using an alpha level of 0.01, should you reject Ho? Briefly explain.