Question

A research team has suggested that men like Pokemon more then women. A group of 270 women and a group of 302 men were asked if they like Pokemon. Out of the group of 270 women, 120 like Pokemon while 216 men like Pokemon.

(a) Calculate the best point estimate for the true value by which the proportion of men that like Pokemon more then women.

(b) Use the data to perform a test of hypothesis at a significance level of 5% of the claim that the sex of the individual effects if they like 5 Pokemon. [Include the critical region, the value of the pivot for the sample data and the corresponding p-value]

Answer 1

a)

The difference in point estimate = 216/302 - 120/270 = 0.7152 - 0.4444 = 0.2708

b)

For sample 1, we have that the sample size is Ni = 270, the number of favorable cases is Xi 120, so then the sample proportion is pi = 20 = 0.4444 For sample 2, we have that the sample size is N2 = 302, the number of favorable cases is X2 216, so then the sample proportion is p2 = 3 0.7152 120-216 0.5874 270+302 The value of the pooled proportion is computed as p N+N 0.05 Also, the given significance level is a (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho pi p2 Ha : py= p2 This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted (2) Rejection Region 0.05, and the critical value for a two- Based on the information provided, the significance level is a = 1.96 tailed test ise The rejection region for this two-tailed test is R = {z : |2| > 1.96 (3) Test Statistics The z-statistic is computed as follows: 0.4444 0.7152 =-6.567 V0.5874 (1-0.5874)(1/270 1/302) VP(1p1/711/n2) (4) Decision about the null hypothesis = 6.567 = 1.96, it is then concluded that the null hypothesis is Since it is observed that rejected 0, and since p= 0 0.05, it is concluded that the Using the P-value approach: The p-value is p null hypothesis is rejected.

(5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p is different than p2, at the 0.05 significance level. Confidence Interval The 95% confidence interval for p - P2 is: -0.349 < p1 -P2 0.193 Graphically Z-test for Two Proportions, z -6.567, p 0 0.40 0.35 0.30- 0.25 0.20- 0.15- 0.10 0.05 0.00 -8 -6 -4 2 2 6