# Can we infer at the 10% significance level that the mean proportion of returns is less than 10%?University bookstores order books that instructors adopt for their courses. The number of copies...

Can we infer at the 10% significance level that the mean proportion of returns is less than 10%?

University bookstores order books that instructors adopt for their courses. The number of copies ordered matches the projected demand. However, at the end of the semester the bookstore has too many copies on hand and must return them to the publisher. A bookstore has a policy that the proportion of books returned should be kept as small as possible. The average is supposed to be less than 10%. To see whether the policy is working, a random sample of book titles was drawn and the fraction of the total originally ordered that are returned is recorded and listed here: 4 15 11 7 5 9 4 3 5 8

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University bookstores order books that instructors adopt for their courses. The number of copies ordered matches the projected demand. However, at the end of the semester the bookstore has too many copies on hand and must return them to the publisher. A bookstore has a policy that the proportion of books returned should be kept as small as possible. The average is supposed to be less than 10%. To see whether the policy is working, a random sample of book titles was drawn and the fraction of the total originally ordered that are returned is recorded and found to be: 4 15 11 7 5 9 4 3 5 8

The average percentage of returns is: (4 + 15 + 11 + 7 + 5 + 9 + 4 + 3 + 5 + 8)/10 = 7.1%

The population standard deviation is 3.5623

The z-score for 10% is (10 - 7.1)/3.5623 = 0.8140

Using a normal table the probability for a z-score of 0.8140 is 0.291

The values that lie in the 10% significance level are above 11.6653.

**This implies that within a 10% percent significance level the mean proportion of returns is less than 10%.**

**Sources:**

The samples are as follows:

4 15 11 7 5 9 4 3 5 8