Final answer:
The student is asking about testing a hypothesis that the proportion of men who believe maintaining a romantic relationship over the Internet is cheating is less than the proportion of women who believe the same. We use the responses of two independent samples and apply a hypothesis test for the difference in proportions at a significance level of 0.05.
Step-by-step explanation:
Testing the Claim About Proportions of Men and Women Who Believe in Internet Cheating
We are tasked with testing the claim that a smaller proportion of men believe maintaining a romantic relationship over the Internet while in an exclusive relationship is cheating, compared to women. To do this, we will perform a hypothesis test for the difference between two proportions at the 0.05 level of significance. The data given includes responses from two independent samples, with 120 out of 184 men saying yes, and 102 out of 136 women saying yes to the question posed.
Null Hypothesis (H0): The proportion of men who believe in internet cheating is the same as or greater than the proportion of women (p_m ≥ p_w).
Alternative Hypothesis (H1): The proportion of men who believe in internet cheating is less than the proportion of women (p_m < p_w).
Using statistical software or a standard statistical test, we would calculate the test statistic for the difference in proportions and compare it to a critical value or find the p-value. If the p-value is less than the significance level of 0.05, we reject the null hypothesis, meaning there is enough evidence to support the claim that a smaller proportion of men believe that such behavior is cheating. If the p-value is higher, we fail to reject the null hypothesis.