Question

The authors of a paper concluded that more boys than girls listen to music at high volumes. This conclusion was based on data from independent random samples of 770 boys and 748 girls from a country, age 12 to 19. Of the boys, 397 reported that they almost always listen to music at a high volume setting. Of the girls, 331 reported listening to music at a high volume setting.

Do the sample data support the authors' conclusion that the proportion of the country's boys who listen to music at high volume is greater than this proportion for the country's girls? Test the relevant hypotheses using a 0.01 significance level. (Use a statistical computer package to calculate the P-value. Use p_boys − p_girls. Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

State your conclusion.

We reject H₀. We have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

We fail to reject H₀.

We have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.    We reject H₀.

We don't have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

We fail to reject H₀. We don't have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country's girls who listen to music at high volume.

Answer 1

H₀: P1 = P2

H₁: P1 > P2

= 397/770 = 0.5156

= 331/748 = 0.4425

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                      = (0.5156 * 770 + 0.4425 * 748)/(770 + 748)

                                                      = 0.48

z = ()/sqrt(P(1 - P)(1/n1 + 1/n2))

   = (0.5156 - 0.4425)/sqrt(0.48 * (1 - 0.48) * (1/770 + 1/748))

   = 2.85

P-value = P(Z > 2.85)

             = 1 - P(Z < 2.85)

             = 1 - 0.9978

             = 0.0022

Since the P-value is less than the significance level(0.0022 < 0.01), so we should reject the null hypothesis.

We reject H_o.

We have convincing evidence that the proportion of the country's boys who listen to music at high volume is greater than the proportion of the country;s girls who listen to music at high volume.