Example 7.2

EXAMPLE 7.2

Significance test for watching traditional television. We want to test whether the average time that U.S. college students spend watching traditional television differs from the reported overall U.S. average of 18- to 24-year-olds at the 0.05 significance level. Specifically, we want to test

H₀: μ = 18.5

H_a: μ ≠ 18.5

Recall that , , and . The test statistic is

= −0.762

This means that the sample mean is slightly more than 0.75 standard deviations below the null hypothesized value . Because the degrees of freedom are , this statistic has the distribution. Figure 7.3 shows that the P-value is , where T has the distribution. From Table D, we see that and .

df = 7
p	0.25	0.20
t*	0.711	0.896

Therefore, we conclude that the P-value is between and . Software gives the exact value as . These data are compatible with a mean of 18.5 hours per week. Under , a difference this large or larger would occur about half the time simply due to chance. There is not enough evidence to reject the null hypothesis at the 0.05 level.