Question

The manufacturer of the ColorSmart-5000 television set claims that 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 395 consumers who have owned a ColorSmart-5000 television set for five years. Of these 395 consumers, 312 say that their ColorSmart-5000 television sets did not need repair, while 83 say that their ColorSmart-5000 television sets did need at least one repair. (a) Letting p be the proportion of ColorSmart-5000 television sets that last five years without a single repair, set up the null and alternative hypotheses that the consumer group should use to attempt to show that the manufacturer’s claim is false. (b) Use critical values and the previously given sample information to test the hypotheses you set up in part a by setting α equal to .10, .05, .01, and .001. How much evidence is there that the manufacturer’s claim is false?

Answer 1

Hi

The answer of the following question is given below as follows :

Ans.A) So first of all we will see the value of H_{​​​​​​o} so that we can do this question easily.

H_{​​​​​​O} = P>_ 0.95

H_{​​​​​​a} = P< 0.95.

Ans.B) Sample size (h) = 395 ----------- Given.

So the Estimated Proportion P^{​​​​​​^} = 318/395

Now we will find out the the value of Test statistics (Z)

below as follows :

Z= P^{​​​​​​^} - P / √P(1-P)h

Now putting the concerned values

318/395 - 0.95 / √0.95-(1-0.95)/395

By solving the above equation we get

-13.216

So the P-value for this test is 0.000000

So according to the calculation and the analysis we can say that we will REJECT H_{​​​​​​o} at each value of Alpha.

Because of the Strong proofs.

I hope I have served the purpose well.

Thanks