Question

Psychologists are interested in finding out what proportion of men and women have ended a budding relationship because a kiss did not go well. A survey was administered to a random sample of adults and asked each individual to disclose whether they ended a budding relationship because a kiss did not go well. The results of the survey are summarized in the table.

	Men	Women
No	45	39
Yes	15	21

a) Identify whether the sampling method used in this study is independent or dependent. Explain.

b) Obtain a point estimate for the proportion of men who have ended a budding relationship because a kiss did not go well. Obtain a point estimate for the proportion of women who have ended a budding relationship because a kiss did not go well.

c) Does the data suggest that a lower proportion of men have ended a budding relationship because a kiss did not go well than women at the ? = 0.05 level of significance? Use the critical value method. (Show all six steps for hypothesis testing.)

d) Estimate the difference in proportion of men and women who have ended a budding relationship because a kiss did not go well with 90% confidence. Does the sample evidence suggest there is a difference between the two population proportions? If so, interpret and describe the difference by identifying which group has a lower proportion.

Answer 1

(a) The study is dependent because each individual was asked to disclose whether they ended a budding relationship because a kiss did not go well.

(b)

p1	p2
0.25	0.35
15/60	21/60

(c) The hypothesis being tested is:

H₀: p₁ = p₂

H_a: p₁ < p₂

The test statistic is -1.20.

The critical value is 1.645.

Since 1.20 < 1.645, we cannot reject the null hypothesis.

Therefore, we cannot conclude that a lower proportion of men have ended a budding relationship because a kiss did not go well than women.

(d) The 90% confidence interval for the difference in the proportion of men and women who have ended a budding relationship because a kiss did not go well is between -0.2368 and 0.0368.

p1	p2	pc
0.25	0.35	0.3	p (as decimal)
15/60	21/60	36/120	p (as fraction)
15.	21.	36.	X
60	60	120	n
	-0.1	difference
	0.	hypothesized difference
	0.0837	std. error
	-1.20	z
	1.6450	critical value
	-0.2368	confidence interval 90.% lower
	0.0368	confidence interval 90.% upper
	0.1368	margin of error