Question

3. [18.76/25 Points] DETAILS PREVIOUS ANSWERS ILLOWSKYINTROSTAT1 10.HW.102. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A recent year was randomly picked from 1985 to the present. In that year, there were 2,058 Hispanic students at a public university out of a total of 12,328 students. At a community college, there were 324 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different? (Use a = 0.05. For subscripts let 1 - the public university, and 2 - the community college.) Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that NOTE: If you are using assumption, though.) Part(a) + Part (b) Part (c) Part (0) State the distribution to use for the test. (Round your answers to four decimal places.) Pi-P2N X Part(e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the distribution round your answer three decimal places.) Part (0) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. If Hois false, then there is a chance equal to the p-value that the difference in the proportion of Hispanic students at the public university and the proportion of Hispanic students at the community college is at least 0.03. If Ho is true, then there is a chance equal to the p-value that the difference in the proportion of Hispanic students at the public university and the proportion of Hispanic students at the community college is at least 0.03. If Ho is true, then there is a chance equal to the p-value that the difference in the proportion of Hispanic students at the public university and the proportion of Hispanic students at the community College is at most 0.03. If Ho is false, then there is a chance equal to the p-value that the difference in the proportion of Hispanic students at the public university and the proportion of Hispanic students at the community college is at most 0.03.

Please help me with d, e, and f. Thanks

Answer 1

(d)

n1 = 12328

$\hat{p}$1 = 2058/12328 = 0.1669

n2 = 2441

$\hat{p}$2 = 324/2441 =0.1327

So,

$\hat{p}1-\hat{p}2=0.1669 - 0.1327=0.0342$

Pooled proportion is given by:

$\bar{p}=\frac{2058+324}{12328+2441}=0.1613$

$SE=\sqrt{0.1613\times (1-0.1613)\times (1/12328+1/2441)}=0.008149$

So,

Distribution to use :

Normal

with mean = $\mu$ = 0.0342

and SD = 0.0081

So,

Answer is:

p1 - p2 = N (0.0342, 0.0081)

(e)

Test Statistic is given by:

$Z=\frac{0.0342}{0.0081}=4.20$

So,

Test Statistic is:

Z = 4.20

(f)

By Technology,

p - value = 0.0000

Correct option:

If H0 is true, then there is a chance equal to the p value that the difference in the proportion of Hispanic students of the public university and the proportion of Hispanic students at the community college is at least 0.03.