Question

According to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no landline) is 37%. Jason claims that the proportion of young American adults who do not have a landline is greater than 37%. He conducts a survey with a sample of randomly selected young American adults and finds that 38% do not have landlines. If we set up our null and alternative hypotheses as follows: H 0 : p = 0.37 H a : p > 0.37 and find that: "p-value"=0.418. Does this provide enough evidence to support Jason’s claim? Use an α=0.05 level of significance. Choose the correct answer below.A. Since the p-value < a, do not reject the null hypothesis. B.Since the p-value > a, do not reject the null hypothesis. C.Since the p-value a, reject the null hypothesis.

Answer 1

Since the p-value >
`\alpha`, do not reject the null hypothesis.

Explanation:

We are given that according to the Pew Research Center, the proportion of the American population who use only a cellular telephone (no landline) is 37%.

Jason claims that the proportion of young American adults who do not have a landline is greater than 37%. He conducts a survey with a sample of randomly selected young American adults and finds that 38% do not have landlines.

Null Hypothesis,
`H_0` : p = 0.37

Alternate Hypothesis,
`H_a` : p > 0.37

We are also provided with significance level,
`\alpha` = 0.05 and p-value = 0.418

Now, the decision rule based on p-value ifs given by;

• If the p-value is more than the level of significance (
  `\alpha`), then we will not reject our null hypothesis or rather accept null hypothesis.

• If the p-value is less than the level of significance (
  `\alpha`), then we will reject our null hypothesis.

So, here P-value = 0.418

`\alpha` = 0.05

Clearly, p-value is more than the level of significance (
`\alpha`), so we will not reject our null hypothesis.

Also, it will be concluded that the Jason claims of the proportion of young American adults who do not have a landline is greater than 37% is not correct.