Question

A researcher wants to test the claim that the proportion of men who watch television regularly is greater than the proportion of women who watch television regularly. She finds that 56 of 70 randomly selected men and 47 of 85 randomly selected women report watching television regularly. A 95% confidence interval for the difference in population proportions is (0.10581, 0.38831). Which of the statements gives the correct outcome of the researcher's test of the claim?

Because the confidence interval is positive, the researcher can conclude the proportion of men and women who watch television regularly is the same.

Because the confidence interval is positive, the researcher can conclude the proportion of men and women who watch television regularly may be the same.

Because the confidence interval is positive, the researcher can conclude there is a greater proportion of women than men who watch television regularly.

Because the confidence interval is positive, the researcher can conclude there is a greater proportion of men than women who watch television regularly.

The researcher cannot draw a conclusion about a claim without performing a significance test.

Answer 1

Null hypothesis: The proportion of men who watch television regularly is the SAME OR LESS than the proportion of women who watch television regularly

Alternate hypothesis: The proportion of men who watch television regularly is greater than the proportion of women who watch television regularly

Because the confidence interval is positive, the researcher can conclude there is a greater proportion of men than women who watch television regularly.

Using excel<data<megastat<hypothesis test

Hypothesis test for two independent proportions
	p1	p2	pc
	0.8	0.5529	0.6645	p (as decimal)
	56/70	47/85	103/155	p (as fraction)
	56.	47.	103.	X
	70	85	155	n
		0.2471	difference
		0.	hypothesized difference
		0.0762	std. error
		3.24	z
		.0006	p-value (one-tailed, upper)
		0.1058	confidence interval 95.% lower
		0.3883	confidence interval 95.% upper
		0.1413	margin of error

Since p-value (0.000) is less than alpha(0.05)

Reject the null hypothesis.

So we accept the alternate hypothesis.