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

2. a) Identify whether the sampling method used in this study is independent or dependent. Explain.
3. 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.
4. 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.)
5. 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.

Please show formula for test statistic used and steps used to retrieve answer for clarity.

Answer 1

a) The sampling method used is in the study is independent , as each individual sampled do not have any affect on any other individual to be sampled .

b) The 2 X 2 contingency table is

	men	women	total
no	45	39	84
yes	15	21	36
total	60	60	120

point estimate of proportion is the sample proportion

sample proportion of men who ended a budding relationship, = 15/60= 0.25

sample proportion of women who ended a budding relationship, = 21/60 =0.35

c) Step 1 :The null hypothesis is

Step 2: The alternative hypothesis is

Step 3 : Test criteria

The critical value of z at level of significance is , zc =- 1.65 ( left  tailed )

Reject H0 if calculated z < -1.65

Step 4:

Test statistic

Test statistic

where

P= (15+21)/120 = 0.30

Q= 1-P =0.70

thus ,

Step5 : Comparison

As calculated z > -1.65

Fail to reject the null hypothesis

Step 6 : Conclusion

At 5% level of significance , there is not enough evidence to conclude that lower proportion of men have ended a relationship than women .

d) The 90% confidence interval for difference in proportion is

= (-0.24 , 0.04)

Since the confidence interval include zero ( lower and upper limit are at two sides of zero)

The difference is not significant

The sample do not provide enough evidence to conclude that lower proportion of men have ended a relationship than women .

Note : For 90% confidence , zc =1.65

Note : The confidence interval is expected to contain true difference in proportion

Thus confidence interval include 0 , means we cannot conclude that the true difference is not zero

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