Answer to Question #236970 in Statistics and Probability for blossomqt

Question

A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchases right out of the box. In its last model, 85% of customers received fully charged batteries. To simulate arrivals, the company shipped 100 new model laptops to various company sites around the country. Of the 105 laptops shipped, 96 of them arrived reading 100% charged. Do the data provide evidence that this model’s rate is at least as high as the previous model? Test the hypothesis at α = 0.05.

Answer 1

QUESTION

A computer manufacturer ships laptop computers with the batteries fully charged so that customers can begin to use their purchases right out of the box. In its last model, 85% of customers received fully charged batteries. To simulate arrivals, the company shipped 100 new model laptops to various company sites around the country. Of the 105 laptops shipped, 96 of them arrived reading 100% charged. Do the data provide evidence that this model’s rate is at least as high as the previous model? Test the hypothesis at α = 0.05.

SOLUTION

$n=105$

$x=96$

Proportion of laptop's arrived with fully charged batteries

$\hat{p}=\frac{96}{105}=0.9142$

$p_o=0.85$

$\alpha=0.05$

$H_0:p\le0.85$

$H_1=p\gt0.85$

Test-statistic for proportion test:

$Z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$

$Z=\frac{0.9142-0.85}{\sqrt{\frac{0.85(1-0.85)}{105}}}=5.826$

P-value estimation. This is a one side test the p value would be:

$p_v=P(Z\gt5.826)=1-P(Z\lt5.826)=1-0.942=0.058$

$\alpha=0.05$

$p_v\gt\alpha$

There is enough evidence to accept the null hypothesis because the data gave the evidence that this model’s rate is NOT higher than the previous model