A marketing agency selected a random sample of television viewers to test the claim that the proportion of viewers who watch a particular show is less than 0.20 at a level of significance of 0.05. The test yielded a p-value of 0.47. Assuming all conditions for inference were met, which of the following is the correct conclusion?

a. At the level of significance of 0.05, the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20
b. At the level of significance of 0.05, the null hypothesis is not rejected. There is convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20.
c. At the level of significance of 0.05, the null hypothesis is rejected. There is convincing evidence to suggest that the true proportion of television viewers who watch the show is less than 0.20.
d. At the level of significance of 0.05, the null hypothesis is rejected. There is not convincing evidence to suggest that the true proportion of television viewers who watch the show is greater than 0.20.
e. At the level of significance of 0.05, the null hypothesis is rejected. There is convincing evidence to conclude that the null hypothesis is true.

Answer:

A) At the level of significance of 0.05, the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20.

Since the calculated p value by the test is obtained higher than that of significance level, thus we cannot reject the null hypothesis.

Thus, option A: At the level of significance of 0.05, the null hypothesis is not rejected. There is not  convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20.

We have following information:

The p value obtained by test = 0.47

The test was conducted to test the claim that the proportion of viewers who watch a particular show is less than 0.20 at a level of significance 0.05.

We have the null hypothesis as

Null hypothesis here = "the proportion of viewers who watch a particular show is equal to 0.20 "

Alternate hypothesis = "the proportion for aforesaid condition is less than 0.20"

Since the obtained p value is more than the level of significance, thus we have the conclusion that we cannot reject the null hypothesis, thus cannot conclude that the proportion for aforesaid condition is less than 0.20.

Thus, option A: At the level of significance of 0.05, the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20.

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