A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week. To test the belief, the scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a p-value of 0.061. The computation of the p - value assumes which of the following is true?

(A) The population proportion of adults who watch 15 or fewer hours of television per week is 0.28. Submit

(B) The population proportion of adults who watch 15 or fewer hours of television per week is 0.30.

(C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

(D) The population mean number of hours adults spend watching television per week is 15.

(E) The population mean number of hours adults spend watching television per week is less than 15.

Question

Mathematics

Alayna

20 July, 15:29

A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week. To test the belief, the scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a p-value of 0.061. The computation of the p - value assumes which of the following is true?

(A) The population proportion of adults who watch 15 or fewer hours of television per week is 0.28. Submit

(B) The population proportion of adults who watch 15 or fewer hours of television per week is 0.30.

(C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

(D) The population mean number of hours adults spend watching television per week is 15.

(E) The population mean number of hours adults spend watching television per week is less than 15.

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Answers (1)

Know the Answer?

Jett Chaney · Answer 1

(C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30

Step-by-step explanation:

Let the proportion of adults watching television less than or equal to 15% be = x

Null Hypothesis [H0] : x = 30% = 0.30 Alternate Hypothesis [H1] : x < 30%, or x < 0.30

P value is calculated at z value : p' - [ √ { p0 (1 - p0) } / n ];

where p' = 0.28, p0 = 0.30, p1 = 0.70; ∴ p (z < - 1.543) = 0.061

Assuming 10% level of significance, p = 0.10

As p value 0.061 < 0.10, we reject H0 & accept H1. This implies that we conclude that 'x ie proportion of adults watching television less than or equal to 15% < 30% or 0.30'