Question

You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 33 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each The results are shown in the table below. At a=0.01, can you support the university's claim? Complete parts (a) through (d) below Assume the population is normally distributed 32 34 28 260 33 36 30 (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states H, and H,? 6 arti OA. HO 1533 H, > 33 OD. HO 1:33 HH33 Ho <33 H, H2 33 Ho = 33 Hu<33 Ho | » 33 H 33 Ho 233 Ha #<33 (b) Use technology to find the P value P (Round to three decimal places as needed) Intes

Answer 1

Solution:
Given in the question
The claim is the mean class size for full-time faculty is fewer than 33 so null and alternative hypothesis can be written as
Null hypothesis H0: $\mu$ = 33
Alternative hypothesis Ha:$\mu$ < 33
So its correct answer is F.
Number of sample = 18
The sample mean = (32+30+31+34+35+40+28+23+26+27+33+37+36+31+25+27+31+25)/18 = 551/18 = 30.6
Sample standard deviation = sqrt($\sum$Xi-mean)^2(n-1))

X	Xi-mean	(Xi-mean)^2
32	1.388888889	1.929012346
30	-0.611111111	0.37345679
31	0.388888889	0.151234568
34	3.388888889	11.4845679
35	4.388888889	19.26234568
40	9.388888889	88.15123457
28	-2.611111111	6.817901235
23	-7.611111111	57.92901235
26	-4.611111111	21.26234568
27	-3.611111111	13.04012346
33	2.388888889	5.706790123
37	6.388888889	40.81790123
36	5.388888889	29.04012346
31	0.388888889	0.151234568
25	-5.611111111	31.4845679
27	-3.611111111	13.04012346
31	0.388888889	0.151234568
25	-5.611111111	31.4845679
	Sum(Xi-mean)^2	372.2777778

Standard deviation =sqrt(372.2778/17) = 4.68
Here we will use a t-test as sample size is small and the population standard deviation is not known. So test stat can be calculated as
Test stat = (Xbar - $\mu$ )/S/sqrt(n)= (30.6-33)/4.68/sqrt(18) = -2.17
So the degree of freedom df = sample size -1 = 18-1 = 17 and this test is left tailed test
From t table, we found a p-value = 0.0222
At alpha = 0.01, we are failed to reject the null hypothesis as the p-value is greater than alpha value, so we don't have significant evidence to support the claim that the mean class size for full-time faculty is fewer than 33.