6.16 More confidence interval mistakes and misunderstandings. Suppose that 100 randomly selected members of the Karaoke Channel were asked how much time they typically spend on the site during the week. The sample mean was found to be 3.8 hours. Assume that the population standard deviation is known to be o = 2.9. (a) Cary Oakey computes the 95% confidence interval for the average time on the site as 3.8 ± 1.96(2.9/100). What is his mistake? (b) He corrects this mistake and then states that "95% of the members spend between 3.23 and 4.37 hours a week on the site." What is wrong with his interpretation of this interval? (c) The margin of error is slightly larger than half an hour. To reduce this to roughly 15 minutes, Cary says that the sample size needs to be doubled to 200. What is wrong with this statement?

Suppose a randomly selected sample of n = 69 men has a mean foot length of x = 28.3 cm, and the standard deviation of the sample is 3 cm. Calculate an approximate 95% confidence interval for the mean foot length of men. (Round the answers to one decimal place.) to cm

4. 5. A sample of 26 Chips Ahoy regular cookies is taken by a Nabisco quality control manager, and it is found that the mean number of chocolate chips per cookie is 20.39. Nabisco knows that the standard deviation, o, is 2.55 for these cookies. Use your calculator to build a 98% confidence interval for the real mean number of chocolate chips per cookie. Then write a sentence or two that interprets your confidence interval. A researcher is collecting data about the SEC (Southeastern Conference) and its student-athletes. If the researcher wants to estimate the mean number of hours spent on required athletic activities by all student-athletes in the conference, then how many student-athletes must be included in the sample to be 98% confident that the sample mean is within 0.4 hour of the population mean? Assume the population standard deviation (o) is 2.41. Use the formula and show all work. 5.

Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 4 inches. The heights of 9 randomly selected students are 72, 61, 65, 64, 61, 67, 71, 63 and 72. x¯ =? Margin of error at 90% confidence level =? 90% confidence interval = [__.__ , __.__]

A researcher is conducting a study to determine the mean trough dosage of medication for a population. Assume a previous study was conducted for the same medication and the mean trough dose was found to be 490 mg with a standard deviation of 30 mg. If the researcher wants to be 95% confident the true mean trough dosage of the medication is within 10 mg of the true mean trough dosage, what sample size is needed if the study is predicted to have an 76% retention rate? n = 50 n = 71 n = 47 n = 104

The mayor is interested in finding a 90% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 185 residents whose mean number of pounds of trash generated per person per week was 34.3 pounds and the standard deviation was 6.4 pounds. Round answers to 3 decimal places where possible. a. With 90% confidence the population mean number of pounds per person per week is between and pounds. b. If many groups of 185 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week and about percent will not contain the true population mean number of pounds of trash generated per person per week.