Answer to Question #214529 in Statistics and Probability for Madimetja

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 100 laptops shipped, 93 of them arrived reading 100% charged. Do the data provide evidence that this model’s rate is higher than the previous model? Test the hypothesis at a = 0:01. Write down the hypothesis to be tested and show all the steps and calculations

Answer 1

$n=100 \\ x=93$

Proportion of laptop's arrived with fully charged batteries

$\hat{p}= \frac{93}{100}=0.93 \\ p_0=0.85 \\ α=0.01 \\ H_0: p≤0.85 \\ H_1: p>0.85$

Test-statistic for proportion test:

$Z= \frac{\hat{p}-p_0}{ \sqrt{ \frac{p_0(1-p_0)}{n} } } \\ Z = \frac{0.93-0.85}{ \sqrt{ \frac{0.85(1-0.85)}{100} } } = 2.24$

P-value estimation.

This is a one side test the p value would be:

$p_v=P(Z>2.24) = 1 – P(Z<2.24) = 1 -0.9874 = 0.0126 \\ α=0.01 \\ p_v>α$

We have enough evidence to accept the null hypothesis.

The data provide evidence that this model’s rate is NOT higher than the previous model.