Final

STAT200 - Final Exam 200 points - Due: Tuesday, December 15th.

Please provide a complete response to each item. Include a sketch, calculations, rationale written using proper statistical language, and any conclusions drawn from the context of the problem, as necessary.

1. Determine whether the discrete random variable is discrete or continuous. In each case, state the possible values of the random variable.

a. The number of students in a randomly selected third-grade classroom.

b. The amount of snow that falls in Delaware during the winter season.

c. The flight time accrued by a randomly selected Air Force fighter pilot.

d. The number of points scored by the Duke Blue Devils during a randomly selected basketball game.

2. The number of chocolate chips in an 18-ounce bag of Chips Ahoy! chocolate chips is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips according to a study by cadets in the U.S. Air Force Academy.

a. What is the probability that a randomly selected 18-ounce bag of Chips Ahoy! contains between 1100 and 1300 chocolate chips, inclusive?

b. What proportion of 18-ounce bag of Chips Ahoy! contains fewer than 1125 chips?

c. What is the percentile rank of an 18-ounce bag of Chips Ahoy! that contains 1350 chocolate chips?

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3. The General Social Survey asked: “How many emails do you send in a day?” The results of 928 respondents indicate that the mean number of emails sent in a day is 10.4 with a standard deviation of 28.5.

a. Given the fact that 1 standard deviation to the left of the mean results in a negative number of emails being sent, what shape would you expect the distribution of emails sent to have?

b. Construct and interpret a 90% confidence interval for the mean number of emails sent per day.

4. Man-ly Muscles? Young men in North America and Europe (but not in Asia) tend to think they need more muscle to be attractive. One study presented 200 young American men with 100 images of men with various levels of muscle. Researchers measured the level of muscle in kilograms per square meter (kg/m​2​) of fat-free body mass. Typical young men have about 20 kg/m​2​. Each subject chose two images, one that represented his own level of body muscle, and one he thought represented “what women prefer.” The mean gap between self-image and “what women prefer” was 2.35 kg/m​2​. Suppose that the “muscle gap” in the population of all young men has a Normal distribution with a standard deviation of 2.5 kg/m​2​. Give a 90% confidence interval for the mean amount of muscle young men think they should have to be attractive to women. Note: A second study was done surveying women, it showed women actually prefer a level close to that of a ”typical man”.

5. More Muscle? If young men thought that their own level of muscle was about what women prefer, the mean “muscle gap”, discussed in a previous exercise, would be 0. We suspect (before seeing the data) that young men think women prefer more muscles than they themselves have.

a. State the null and alternative hypotheses for testing this suspicion.

b. What is the value of the test statistic ​z​ ?

c. State a complete conclusion.

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6. According to the Centers for Disease Control and Prevention, 16.8% of high school students currently use electronic cigarettes. A high school counselor is concerned that the use of e-cigs at his school is actually higher.

a. Determine the null and alternative hypotheses.

b. If the sample data indicate that the null hypothesis should not be rejected, state the conclusion of the school counselor.

.

7. In December 2005, 38% of adults with children under the age of 18 reported that

their family ate dinner together seven nights a week. In a recent poll, 503 of 1232 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Has the proportion of families with children under the ages of 18 who eat dinner together seven nights a week increased? Test at the 0.05 significance level.

8. Researchers at Harris Interactive wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and females, the following question:

“Are you annoyed by people who repeatedly check their mobile phones while having an in-person conversation?”

● Among the 540 males surveyed, 178 responded “Yes” ● Among the 560 females surveyed, 206 responded “Yes”

a. Does the evidence suggest a higher proportion of females are annoyed by

this behavior? State the null and alternative hypotheses?

b. Determine and interpret the p-value.

c. At the 0.05 level of significance, what is the conclusion of the hypothesis test?

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9. A researcher for the U.S. Department of Treasury wishes to estimate the

percentage of Americans who support abolishing the penny. What size sample should be obtained if she wishes the estimate to be within 2 percentage points with 98% confidence level, if:

a. she uses a 2006 estimate of 28% obtained from a Coinstar National

Currency Poll?

b. she does not use any prior estimate?

10. The following data represent the number of days absent from class, ​x​, and the final grade, ​y​, for a sample of college students grade in an introductory statistics course at a large state university.

a. Find the least-squares regression line treating the number of absences as the explanatory variable and final grade as the response variable.

b. Interpret the slope and y-intercept, as appropriate.

c. Predict the final grade for a student who misses five class periods and compute the residual. Is the final grade above or below average for this number of absences?

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No. of absences, ​x

0

1

2

3

4

5

6

7

8

Final grade, ​y

92.4

88.4

83.5

77.4

73.2

68.8

67.5

60.0

55.0