The manufacturer of the ColorSmart-5000 television set claims that 95 percent of
ID: 3274971 • Letter: T
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 410 consumers who have owned a ColorSmart-5000 television set for five years. Of these 410 consumers, 313 say that their ColorSmart-5000 television sets did not need repair, while 97 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.
H0 :p (Click to select)<> .95 versus Ha : p (Click to select)>< .95.
(b) Use critical values and the previously given sample information to test the hypotheses you set up in part a by setting equal to .10, .05, .01, and .001. How much evidence is there that the manufacturer’s claim is false?
(Click to select)RejectDo not reject H0 at each value of ; (Click to select)very strong nonestrong someextremely strong evidence.
Explanation / Answer
a) H0 :p>=0.95
Ha : p <0.95
b) critical value for .10, .05, .01, and .001 are respectively -1.28 , -1.645 ,-2.326 and -3.09.
here p=0.95 ; n=400
std error =(p(1-p)/n)1/2 =0.0109
phat =313/400=0.7825
therefore test stat z=(phat-p)/std error =(0.7825-0.95)/0.0109 =-15.3709
as test stat is below all critical values;
therefore Reject H0 at each value of )very strong evidence.
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