Practice calculating and interpreting the different types of confidence interval

Jun 12th, 2015
Anonymous
Category:
Mathematics
Price: $10 USD

Question description

22. You Explain It! Superstition: A USA Today/Gallup poll asked 1,006 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 adult Americans who would be bothered to stay in a room on the 13th floor is between 0.10 and 0.16.

Answer:

(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.

Answer:

(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.

Answer:

(d) We are 95% confident that 13% of adult Americans would be bothered to stay in a room on the 13th floor.

Answer:

Section 9.2

8. (a)  Find the t-value such that the area in the right tail is 0.02 with 19 degrees of freedom.

Answer:

(b) Find the t-value such that the area in the right tail is 0.10 with 32 degrees of freedom.

Answer:

(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.]

Answer:

(d) Find the  critical t-value  that  corresponds to  95% confidence. Assume 16 degrees of freedom.

Answer:

Section 9.3

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.

Answer:

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.

Answer:


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