Chapter 12.6, Problem 26PPS

To determine

To conduct: A hypothesis test.

Answer to Problem 26PPS

It is conclude that batteries last less than 8 hours.

Explanation of Solution

Given information:

The following data represents Grace Calculation.

8.1	7.9	7.8	8.0	8.2	7.8	7.7	8.1	7.8	7.7
8.2	8.4	8.2	7.8	7.7	7.7	7.9	8.3	8.1	8.0
8.0	7.9	7.9	8.4	8.1	8.2	8.0	7.6	7.7	7.9
7.8	7.9	8.0	8.0	8.1	8.1	8.2	7.6	7.8	7.8
8.0	8.1	8.1	7.9	7.9	7.9	8.1	7.8	7.8	8.0

Hypotheses are,

  $\begin{array}{l}{H}_0:\mu =8\hfill \\ H_1:\mu <8\hfill \end{array}$

Grace tests 50 different batteries. And test the hypothesis using 95% confidence interval.

Grace collects the data for 50 batteries. Here using excel functions"=average ()" for mean and "stdev()" for standard deviation the information for finding 95% confidence interval is,

  $\overline{x}=7.96,s=0.194,n=50$

The 95% confidence interval for mean is,

  $\begin{array}{l}\overline{x}\pm 1.96\cdot \frac{s}{\sqrt{n}}=7.96\pm 1.96\cdot \frac{0.194}{\sqrt{50}}\\ \begin{array}{l}=7.96\pm 0.05\hfill \\ =\left(7.91,7.81\right)\hfill \end{array}\end{array}$

Since confidence interval does not contain 8 so, one can reject the null hypothesis. That is one can conclude that batteries last less than 8 hours.