Question

Since the end of The Mandalorian, 65% of parents (N=100) and 46% of non-parents (N=100) are subscribed to Disney+. Test the null hypothesis that parents and non-parents are equally likely to subscribe to Disney+ (alpha=0.05).

Answer 1

The value of the pooled proportion is computed as

Also, the given significance level is α=0.05.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: ​

Ha: ​

This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is zc​=1.96.

The rejection region for this two-tailed test is R={z:∣z∣>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

(4) The decision about the null hypothesis

Since it is observed that ∣z∣=2.703>zc​=1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0069, and since p=0.0069<0.05, it is concluded that the 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 p1​ is different than p2​, at the 0.05 significance level.

Graphically