Question

An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be​ minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the proportion of damaged machines below 2% One day an inspector randomly checks 66 washers and finds that 6 of them have scratches or dents. Is this strong evidence that the warehouse is failing to meet the company​goal? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are satisfied before you proceed.

1) What is the value of the test statistic? If applicable

2) What is the​ P-value of the test​ statistic? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. If applicable

3) What is your​ conclusion? Assume alpha = 0.05.

- his is strong evidence that less than 2% get damaged

- his is strong evidence that more than 2% get damaged

-This is not strong evidence that more than 2% get damaged

-The assumptions and conditions are not​ met, so the test cannot proceed.

2 %

Answer 1

Answer:

This is strong evidence that more than 2% get damaged

Step-by-step explanation:

The company goal is to keep the proportion of damaged machines below 2%

$H_o: p = 0.02$

$H_a: p > 0.02$

One day an inspector randomly checks 66 washers and finds that 6 of them have scratches or dents

So, x = 6

n = 66

$\widehat{p}=\frac{x}{n}$

$\widehat{p}=\frac{6}{66}$

Formula : $z=\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$z=\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

$z=\frac{\frac{6}{66}-0.02}{\sqrt{\frac{0.02(1-0.02)}{66}}}$

$z=4.114$

So, the value of test statistic is 4.114

2)  What is the​ P-value of the test​ statistic?

So, p value using calculator =  .00002

p value < α

So, we accept the alternate hypothesis

So, This is strong evidence that more than 2% get damaged