In: Statistics and Probability
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 767 boys and 750 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
pboys − pgirls. 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.