Question

The attached data contains a sample of undergraduate institutions in the US along with information about the size of their undergraduate enrollment. Your goal is to (1) construct a confidence interval for the true population proportion of undergraduate institutions with enrollment over 1000, and (2) to perform a hypothesis test on the claim that less than half of the undergraduate institutions in the US have an enrollment over 1000 (using an α = 0.05 significance level)

# OF UNDERGRADS
50
3567
833
3595
149
79
123
223
633
83
7983
251
600
1586
1672
76
165
141
111
8
271
393
581
111
323
8
95
1651
875
6162
11232
991
817
15975
452
832
1705
35
8284
230
722
19870
45
185
74
352
11557
943
6348
5977
13
5501
89
16048
4873
176
1565
2320
2558

a) Calculate the sample proportion, sample size and critical value (5 pts)		p_hat
		n
		z*

b) Calculate the margin of error (5 pts)		MoE

c) Calculate the bounds on the confidence interval (5 pts)		lower bound
		upper bound

b) Calculate the margin of error (5 pts)		MoE

Answer 1

2 we have to test Hoip > 0.5 vs Hiipcois we have p=0.3621n=58 Po=0.5 Pege npo=5880.5=29 a nit Pol = 29 >l here alternative hypothesis is less than type. Therefore given test is left failed test z test for one population propertiem We use A critical value: x=0.os Z = 70.05 = 1.6449 Test statistic 0.3621-0.5 -2.1004 Poll-po) 0:5(1-0.5) 58. P - Po Decision Rule : Reject Ho if zc-.2x here z L-22 i.e - 2.1004 <- 1.6449 : we reject Ho at sy level of significance conclusion: We reject Ho and there is sufficient evidence to conclude that less than half ofs undergradu -ate institution in the us have enrollment over 1000 sl significance level. cet