Question

Perform these hypothesis tests. Show the formulas for the test statistics and what numbers go into them. Clearly show your decision, write it in words, and be sure to write out your null and alternative hypotheses. In a study of 40 heterosexual couples, 28 of the 40 couples the male said “I love you” first. The researchers were interested in learning whether these data provided evidence that in significantly more than 50% of these couples the male says “I love you” first.

Answer 1

We will test the hypothesis at 0.05 significance level

We are provided with proportions in the questions, so it is clearly a z proportion hypothesis testing case.

We have

sample size n = 40

sample proportion = 28/40 = 0.70

population proportion = po = 0.50

We have to test the claim whether more than 50% of these couples the male says "I love you" first.

So, null hypothesis will be that exactly or less than 50% said "I love you" first. and alternate hypothesis will be that more than 50% said "I love you" first.

Formula for z test statistic is given as

setting the given values, we get

this gives us

z = 0.20/0.079 = 2.53

Using z distribution table for z value = 2.53 and significance level 0.05, we get the required p value

p value = 0.0057

So, it is clear that the p value is less than significance level of 0.05, rejecting the null hypothesis. Thus, we can conclude that more than 50% of these couples the male said "I love you" first.