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 405 consumers who have owned a ColorSmart-5000 television set for five years. Of these 405 consumers, 318 say that their ColorSmart-5000 television sets did not need repair, while 87 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 H_a : 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 α equal to .10, .05, .01, and .001. How much evidence is there that the manufacturer’s claim is false?

Reject or Do not reject H₀ at each value of α; (Click to select)
strong
very strong
none
some
extremely strong

evidence.

Answer 1

Ans:

a)

H₀:p>=0.95

H_a:p<0.95

sample proportion=318/405=0.7852

Test statistic:

z=(0.7852-0.95)/SQRT(0.95*(1-0.95)/405)

z=-15.22

b)critical z value=-2.33

Reject  H₀ ,at each value of α

extremely strong evidence.