Acell phone store has sold 150 phones of brand a and had 14 returned as defective. additionally it has sold 125 phones of brand b and had 15 returned as defective. is there statistical evidence that brand a has a smaller chance of being returned than brand b? use the 5-step method.

So the p value is a very high value and using any significance level for example we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of defective from Brand B  is NOT significantly higher than the proportion of of defective from Brand A  

Step-by-step explanation:

1) Data given and notation  

represent the number of returned from brand A

represent the number of returned from brand B

sample for Brand A selected

sample for Brand B selected

represent the proportion of returned from brand A

represent the proportion of returned from brand B

z would represent the statistic (variable of interest)  

represent the value for the test (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion of defective for Brand B is higher than for Brand A , the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

We need to apply a z test to compare proportions, and the statistic is given by:  

  (1)

Where

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

4) Statistical decision

For this case we don't have a significance level provided , but we can calculate the p value for this test.  

Since is a one right tailed test the p value would be:  

5) Conclusion

So the p value is a very high value and using any significance level for example we see that so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of defective from Brand B  is NOT significantly higher than the proportion of of defective from Brand A  

146%

step-by-step explanation:

probability for j is 1/4

while

a is 1/6