Question

A quality control expert at a pretzel factory took a random sample of 10 bags from a production run of over 500 bags and measured the amount of pretzels in each bag in the sample. The sample data were roughly symmetric with a mean of 450 and a standard deviation of 15 g. Based on this sample, which of the following is a 90% confidence interval for the mean amount of pretzels per bag (in grams) in this production run?

A. 450 ± 4.743
B. 450 ± 7.803
C. 450 ± 8.695
D. 450 ± 15
e. 450 ± 27.495

Answer 1

C. 450 ± 8.695

Explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 10 - 1 = 9

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of
. So we have T = 1.8331

The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.

Confidence interval is sample mean plus/minus margin of error. So

The correct answer is given by option C.