Stats Assignment

Question 1

The total sleep time per night among college students is approximately Normally distributed with mean hours and standard deviation hours. You plan to take an SRS of size and compute the average total sleep time.

1. What is the standard deviation of the average time?
2. Use the 95 part of the Empirical Rule (68-95-99.7 rule) to describe the variability of this sample mean.
3. What is the probability that your average will be below 6.8 hours?

Question 2

Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency, or gas mileage, usually expressed as miles per gallon (mpg). For one vehicle equipped in this way, the miles per gallon were recorded each time the gas tank was filled, and the computer was reset. Here are the mpg values for a random sample of 20 of these records:

Suppose that the standard deviation is known to be mpg.

1. What is , the standard deviation of ?
2. Examine the data for skewness and other signs of non-Normality. Show your plots and numerical summaries. Do you think it is reasonable to construct a confidence interval based on the Normal distribution? Explain your answer.
3. Give a 95% confidence interval for , the mean miles per gallon for this vehicle.

Question 3

Corporate advertising tries to enhance the image of corporation. A study compared two ads from two sources, the Volkskrant and the Telegraaf . Subjects were asked to pretend that their company was considering a major investment in Prestomax, the fictitious sportswear firm in the ads. Each subject was asked to respond to the question "How trustworthy was the source in the sportswear company ad for Prestomax?"on a 7-point scale. Higher values indicate more trustworthiness. Here is a summary of the results:

1. Compare the two sources of ads using a t test. Be sure to state your null and alternative hypotheses, the test statistic with degrees of freedom, the P-value and your conclusion.
2. Give a 95% confidence interval for the difference.
3. Write a short paragraph summarizing the results of your analysis.

Question 4

A survey reported that 14% of Dutchman consume five or more servings of soft drinks per week. The data were obtained by an online survey of 1987 randomly selected Dutchman over 15 years of age.

1. What number of survey respondents reported that they consume five or more servings of soft drinks per week? You will need to round your answer. Why?
2. Find a 95% confidence interval for the proportion of Dutchman who report that they consume five or more servings of soft drinks per week.
3. Convert the estimate and your confidence interval to percentages.
4. Discuss reasons why the estimate might be biased.

Question 5

In the 1920s about 97% of US colleges and universities required a physical education course for graduation. Today, about 40% require such a course. A recent study of physical education requirements included 354 institutions: 225 private and 129 public. Among the private institutions, 60 required a physical education course, while among the public institutions, 101 required a course.

1. What are the explanatory and response variables for this example? Explain your answer.
2. What are the populations?
3. What are the statistics?
4. Use a 95% confidence interval to compare the private with the public institutions with regard to the physical education requirement.
5. Use a significance test to compare the private with the public institutions with regard to the physical education requirement.
6. For parts d) and e), verify that the guidelines for using the large-sample methods are satisfied.
7. Summarize your analysis of these data in a short paragraph.

Question 6

A nationally representative survey if students in grades 7 to 12 asked about the experience of these students with respect to sexual harassment. The students were asked whether or not they were harassed in person and whether or not they were harassed online. Here are the data for boys:

1. Analyze these data using a Chi-squared analysis.
2. Analyze these data using the z test for comparing to proportions.
3. Use this example to explain the relationship between the chi-square test and the z test for comparing to proportions.

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Solution: The downloadable solution consists of 10 pages, 1825 words and 1 charts.
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