# Interval Construct/Estimate a Population Mean/Estimate the Value of a Parameter

22. 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.

36. 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?

8. ( 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.

24. 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.

7. 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.

12. 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.

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The solution provides step by step method for the calculation of confidence interval and sample size. Formula for the calculation and Interpretations of the results are also included. The solution serves as a model which can be followed for similar questions.