7. Sampling Distributions & Confidence Intervals: Mean

A puzzle company is interested in the average number of pieces in their jigsaw puzzles, so they plan to create a confidence interval for the true mean. The easiest puzzle in their line is $100$ pieces, and the largest is $1000$ pieces. Use the range rule of thumb to estimate the sample standard deviation.

A bookstore is interested in the average length of books in its adult fiction section. Find the minimum sample size required to create a $99\%$ confidence interval with a margin of error no more than $30$ pages if...

(A) The standard deviation is known to be about $96$ pages.

A bookstore is interested in the average length of books in its adult fiction section. Find the minimum sample size required to create a $99\%$ confidence interval with a margin of error no more than $30$ pages if...

(B) The standard deviation is unknown, but the longest book is $697$ pages and the shortest is $298$ pages.

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̄, is found to be 108, and the sample standard deviation, s, is found to be 10.

b. Construct a 96% confidence interval for μ if the sample size, n, is 10. How does decreasing the sample size affect the margin of error, E?

Reading A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books.

a. How many subjects are needed to estimate the number of books Americans read the previous year within four books with 95% confidence?

Reading A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books.

b. How many subjects are needed to estimate the number of books Americans read the previous year within two books with 95% confidence?

Reading A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books.

c. What effect does doubling the required accuracy have on the sample size?