Question

PART A

1. Consider this hypothesis test:

H0: p1 - p2 = < 0 Ha: p1 - p2 > 0

Here p1 is the population proportion of “yes” of Population 1 and p2 is the population proportion of “yes” of Population 2. Use the statistics data from a simple random sample of each of the two populations to complete the following: (8 points)

	Population 1	Population 2
Sample Size (n)	500	700
Number of “yes”	400	560

1. Compute the test statistic z.
2. What is the p-value?
3. Should H0 be rejected? Use the p-value and a level of significance of 0.05

to justify your answer.

4. Use the above data to construct a 95% confidence interval for p1 - p2

Answer 1

Solution:

Given:

	Population 1	Population 2
Sample size n	500	700
Number of "yes"	400	560

Null and alternative hypothses:

We can find all the things using megastat,

Output is:

Hypothesis test for two independent proportions
	p1	p2	pc
	0.8	0.8	0.8	p (as decimal)
	400/500	560/700	960/1200	p (as fraction)
	400.	560.	960.	X
	500	700	1200	n
		0.	difference
		0.	hypothesized difference
		0.0234	std. error
		0.00	z
		.5000	p-value (one-tailed, upper)
		-0.0459	confidence interval 95.% lower
		0.0459	confidence interval 95.% upper
		0.0459	margin of error

a) Test statistic z = 0.00

b)P-value = 0.5

c) Decision: P-value =0.5 >=0.05, fail to reject H0.

Conclusion: There is not enough evidence to conclude that p1-p2>0 at level of significance =0.05

d)

The 95% confidence interval for p1 - p2 is:

-0.0459 < p1 - p2 < 0.0459

Done