Practice Problems and Solutions in Statistics

Question 1: Estimation of the Percentage of Adults Who Get News Online

1. In a Harris poll of 2036 adults, 40% said that they prefer to get their news online. Construct a 95% con dence interval estimate of the percentage of all adults who say they prefer to get their news online. (10 points)
2. Find the minimum sample size required to estimate the mean pulse rate of adult males with 99% con dence that the sample mean is within 2 bpm of the population mean. Assume = 11:3 bpm. (10 points)
3. Table 1 below lists the waiting times (in minutes) of customers at Wells Fargo Bank, where customers enter a single waiting line that feeds three teller windows. Construct
a 95% con dence interval for the population standard deviation. 

4. It is claimed that fewer than 90% of adults have a cell phone, and in a hypothesis test, the P-value is found to be 0.0003. Brie y interpret the exact meaning of this P-value, and make sure to use terms such as probability and Type I/II error in the context of the original claim. (10 points)
5. When 40 people used the Weight Watchers diet for one year, their mean weight loss was 3.0 lb and the standard deviation was 4.9 lb (Dansinger et al.). Perform a hypothesis test at the 0.01 level of signi cance on the claim that the mean weight loss is greater than 0. Be sure to clearly state the hypotheses, the testing procedure that is relevant and how you know that you are allowed to use it, and include a formal conclusion. (10 points)
6. Couples were recruited for a study of how many words people speak in a day. A random sample of 56 males resulted in a mean of 16,576 words and a standard deviation of 7871 words. Use a 0.01 level of signi cance to test the claim that males have a standard deviation greater than the standard deviation of 7460 words for females. Be sure to clearly state the hypotheses, the testing procedure that is relevant and how you know that you are allowed to use it, and include a formal conclusion. (10 points)
7. Severe carpal tunnel syndrome can be treated with either surgery or wrist splints. In a randomized controlled trial, 73 patients were treated with surgery and 67 of them had successful treatment. Among 83 patients treated with splints, 60 of them had successful treatment. At a 0.01 level of signi cance, test the claim that the success rate is better with surgery. Be sure to clearly state the hypotheses, the testing procedure that is relevant and how you know that you are allowed to use it, and include a formal conclusion. (10 points)
8. Table 2 below lists two sets of randomly collected student evaluation scores for male and female professors. Test the claim that female and male professors have the same mean evaluation scores. Be sure to clearly state the hypotheses, the testing procedure that is relevant and how you know that you are allowed to use it, and include a formal conclusion. (10 points)
9. Suppose that for Table 2: Student evaluation scores for female and male professors, two values were inexplicably missing from the random sample of female professor scores, so that the sample sizes should have actually been equal. Would it be valid to apply a matched-pairs t test procedure? Brie y explain why or why not. 
10. Refer to Table 2: Student evaluation scores for female and male professors again. Use

a 0.05 level of signi cance to test the claim that female and male professors receive scores with the same variance. Be sure to clearly state the hypotheses, the testing procedure that is relevant and how you know that you are allowed to use it, and include a formal conclusion.