Question

A report described teens' attitudes about traditional media, such as TV, movies, and newspapers. In a representative sample of American teenage girls, 42% said newspapers were boring. In a representative sample of American teenage boys, 45% said newspapers were boring. Sample sizes were not given in the report.

(a) Suppose that the percentages reported had been based on a sample of 50 girls and 60 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Use p_girls − p_boys. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State your conclusion.

We fail to reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We fail to reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.    

We reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

(b) Suppose that the percentages reported had been based on a sample of 2050 girls and 2800 boys. Is there convincing evidence that the proportion of those who think that newspapers are boring is different for teenage girls and boys? Carry out a hypothesis test using

α = 0.05.

(Use a statistical computer package to calculate the P-value. Use μ_girls − μ_boys. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State your conclusion.

We fail to reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We fail to reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.   

We reject H₀. We do not have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

We reject H₀. We have convincing evidence that the proportion of girls who say that newspapers are boring is different from the proportion of boys who say that newspapers are boring.

(c) Explain why the hypothesis tests in parts (a) and (b) resulted in different conclusions.

You are much less likely to get a difference in sample proportions as large as the one given when the samples are very large.

You are much less likely to get a difference in sample proportions as large as the one given when the number of boys vs. girls sampled are far apart.   

You are much less likely to get a difference in sample proportions as large as the one given when the number of boys vs. girls sampled are close together.

You are much less likely to get a difference in sample proportions as large as the one given when the samples are very small.

Answer 1

a)

b)

c)

You are much less likely to get a difference in sample proportions as large as the one given when the samples are very large.