Discussion:
Q1. You Explain It! Superstition A USA Today/ Gallup poll asked l006 adult Americans how much it would bother them to stay in a room on the 13th floor of a hotel. Interestingly, 13% said it would bother them. The margin of error was 3 percentage points with 95% confidence. Which of the following represents a reasonable interpretation of the survey results? For those not reasonable, explain the flaw.
(a) We are 95% confident that the proportion of adultAmericans who would be bothered to stay in a room on the 13th floor is between 0.10 and 0.16.
(b) We are between 92% and 98% confident that 13% of adult Americans would be bothered to stay in a room on the 13th floor.
(c) In 95% of samples of adult Americans, the proportion who would be bothered to stay in a room on the 13th floor is between 0.10 and 0.16.
(d) We are 95% confident that 13% of adult Americans would be bothered to stay in a room on the 13th floor.
Q2. Credit- Card Debt A school administrator is concerned about the amount of credit- card debt that college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have credit- card debt of $ 2000 or more. What size sample should be obtained if she wishes the estimate to be within 2.5 percentage points with 94% confidence if
(a) a pilot study indicates that the percentage is 34%?
(b) no prior estimates are used?
Q3. (a) Find the t- value such that the area in the right tail is 0.02 with 19 degrees of freedom.
(b) Find the t- value such that the area in the right tail is 0.10 with 32 degrees of freedom.
(c) Find the t- value such that the area left of the t- value is 0.05 with 6 degrees of freedom. [ Hint: Use symmetry.]
(d) Find the critical t- value that corresponds to 95% confidence. Assume 16 degrees of freedom.
Q4. You Explain It! Sleeping A 90% confidence interval for the number of hours that full- time college students sleep during a weekday is lower bound: 7.8 hours and upper bound: 8.8 hours. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw.
(a) 90% of full- time college students sleep between 7.8 hours and 8.8 hours.
(b) We are 90% confident that the mean number of hours of sleep that full- time college students get any day of the week is between 7.8 hours and 8.8 hours.
(c) There is a 90% probability that the mean hours of sleep that full- time college students get during a weekday is between 7.8 hours and 8.8 hours.
(d) We are 90% confident that the mean hours of sleep that full- time college students get during a weekday is between 7.8 hours and 8.8 hours.
Q5. Aggravated Assault In a random sample of 40 felons convicted of aggravated assault, it was determined that the mean length of sentencing was 54 months, with a standard deviation of 8 months. Construct and interpret a 95% confidence interval for the mean length of sentence for an aggravated assault conviction. Source: Based on data from the U. S. Department of Justice.
Q6. Theme Park Spending In a random sample of 40 visitors to a certain theme park, it was determined that the mean amount of money spent per person at the park ( including ticket price) was $ 93.43 per day with a standard deviation of $ 15. Construct and interpret a 99% confidence interval for the mean amount spent daily per person at the theme park.