Question

Problem 5. In a study designed to assess whether similar gender biases are already present in young boys and girls, O'Neill and Boulton (1996) conducted interviews with 72 female and 81 male children between the ages of 9 and 11 residing in north-west England. Among the questions asked of these youngsters was a question regarding whether or not it was inappropriate for boys or girls to play flute. Within the 72 females, 35 stated that flute should not be played by boys, while no one of them stated that flute should not be played by girls. Within the 81 males, 36 stated that flute should not be played by boys, while 1 stated that flute should not be played by girls. Find the approximate P-value for a test of the hypothesis that both girls and boys agree that boys should not play the flute against the general alternative that they disagree on that issue. > qt (0.5158, (81+72)) [1] 0.03967997 >qnorm (0.5158) (1] 0.03961509 > pnorm (0.5158) [1] 0.6970029 > pt (0.5158, (81+72))

Answer 1

The hypothesis test is performed in following steps,

Step 1: The null and alternative hypothesis are,

0

HA: PI P2

Where,

35 0.4861 P1 72

36 0.4444 P2 81

Step 2: The significance level level,

0.05

The z-test is used to compare two population proportion.

Step 3: The z-statistic is,

P1-P2 P(1 - P) n2 ni

Where,

35 +36 0.4641 72 81

0.4861 0.4444 0.5158 V0.4641(0.4641)

Step 4:

The P-value for the z-statistic is obtained from z distribution table for z = 0.5158

P-value 0.6970029

Since the p-value is greater than 0.05, the null hypothesis is not rejected.