Question

IAB conducted a study of U.S. online adults that included 416 tablet owners. The study found that 221 tablet owners use their tablet while watching TV, TV Experience - Attitudes and Usage across Multiple Screens - The authors of the report imply that the survey proves that more than half of all tablet owners use their tablet while watching TV at least once per day.

1. Use the five-step p-value approach to hypothesis testing and a 0.05 level of significance to try to prove that more than half of all tablet owners use their tablet while watching TV at least once per day.
2. Based on your result in (a), is the claim implied by the authors valid?
3. Suppose the study found that 242 tablet owners use their tablet while watching TV at least once per day. Repeat parts (a) and (b).
4. Compare the results of (b) and (c).

Answer 1

a.

Let p be the true proportion of tablet owners who use their tablet while watching TV.

Null Hypothesis H0: p = 0.5

Alternative Hypothesis H0: p > 0.5

np(1-p) = 416 * 0.5 * (1 - 0.5) = 104

Since, np(1-p) > 10, the sample size is large enough to assume that the sampling distribution of proportion is normal and we can use one sample z test.

Significance level = 0.05

Decision - Reject null hypothesis H0 if p-value is less then 0.05.

Standard error of mean, SE = = 0.0245

Sample proportion, = 221/416 = 0.53125

Test statistic, z = ( - p) / SE = (0.53125 - 0.5) / 0.0245 = 1.28

P-value = P(z > 1.28) = 0.1

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that the true proportion of tablet owners who use their tablet while watching TV is greater than 0.5

b.

Based on the result, the claim implied by the authors is not valid.

c.

Sample proportion, = 242/416 = 0.5817

Test statistic, z = ( - p) / SE = (0.5817 - 0.5) / 0.0245 = 3.33

P-value = P(z > 3.33) = 0.0004

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is strong evidence that the true proportion of tablet owners who use their tablet while watching TV is greater than 0.5

Based on the result, the claim implied by the authors is valid.

d.

The claim of the author is valid, if we found that 242 tablet owners use their tablet while watching TV out of  416 tablet owners. If the  221 tablet owners use their tablet while watching TV, the claim of the author is not valid.