Question

A computer company claims that the lifespan of its batteries is 2.7 years. The population standard deviation is 0.85 years. A sample of 25 batteries was tested, and their mean lifespan was 3.1 years. Using a 95% confidence level, determine if the company's claim is correct.Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.Reject the null hypothesis. There is not enough evidence to oppose the company's claim.Reject the null hypothesis. There is enough evidence to oppose the company's claim

Answer 1

Given

$\begin{gathered} \bar{x}=3.1 \\ \sigma=0.85 \\ \alpha=0.05 \\ n=25 \end{gathered}$

Compute the z statistic;

$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}$$z=\frac{\frac{3.1-2.7}{0.85}}{\sqrt[]{5}}=0.094$

Using a table to compute the p value, we have;

$p=0.92511>0.05$

Thus, we fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim