Chapter 12.6, Problem 28PPS

To determine

To Conduct: A hypothesis test with the help of given information.

Explanation of Solution

Given information:

The label on Leah's can of sliced peaches promises 12 slices in every can. Leah decides to test her hypothesis that there are more than 12 slices in every can by finding the number in 40 random cans.

Use the data below to conduct a hypothesis test:

13	14	13	14	12	12	12	11	15	12
13	13	14	13	14	12	15	11	11	14
13	14	14	13	12	12	12	12	13	13
11	14	14	13	14	13	13	14	12	12

Hypotheses are,

  $\begin{array}{l}{H}_0:\mu =12\hfill \\ H_1:\mu >12\hfill \end{array}$

Leah tests 40 different cans of sliced peaches.And test the hypothesis using 95% confidence interval.

Leah collects the data for 40 random can.Here using excel functions "=average()" for mean and "=stdev()" for standard deviation the information for finding 95% confidence interval is,

  $\overline{x}=12.8,s=1.126,n=40$

The 95% confidence interval for mean is,

  $\begin{array}{l}\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}=12.8\pm 1.96\cdot \frac{1.126}{\sqrt{40}}\\ \begin{array}{l}=12.8\pm 0.349\hfill \\ =\left(12.451,13.149\right)\hfill \end{array}\end{array}$

Since confidence interval does not contain 12 so,one can reject the null hypothesis.That is one can conclude that there are more than 12 slices in every can.