Question

GPA IQ 3.68 126 3.10 105 2.72 104 3.61 118 Math 13 Quiz Chapte 4.0 126 The data below comes from a university that wanted to see if there was a relationhip between IQ score students after their freshman year. Use the data for questions 1 through 5 3.89 154 For each hypothesis test, provide the daim, aitical vakues, test statistk and conclusion 1) Using a 95% level of confidence, test the claim that I's have a mean of 100 3.51 118 2.64 98 2) Using a 95N level of confidence, test the claim that the majority of students have at least a 3.0 GPA 3.33 108 3.32 108 3) At the 98% confidence level, test the claim that mean GPA for freshmen is over 3.0 2.91 95 4)Test the daim that the standard deviation for IQ scores is 15. 3.81 113 3.53 128 S) Divide the data into two groups: those with under a 110 IQ and those with at least 110 IQ 3.95 134 Test the claim that the mean GPA is 10for those with under a 110 1 a) 3.57 116 b Test the daim that the mean GPA is 3.0 for those with at least 110 10 3.22 103 4.0 119 2.32 104 2.65 100 3.42 116 3.55 123 2.94 95 2.75 105 2.6 107 3.56 133

Answer 1

multiple sub-parts. solving first 4

	IQ	GPA
	126	3.68
	105	3.1
	104	2.72
	118	3.61
	126	4
	154	3.89
	118	3.51
	98	2.64
	108	3.33
	108	3.32
	95	2.91
	113	3.81
	128	3.53
	134	3.95
	116	3.57
	103	3.22
	119	4
	104	2.32
	100	2.65
	116	3.42
	123	3.55
	95	2.94
	105	2.75
	107	2.6
	133	3.56
Total	2856	82.58
Mean	114.24	3.3032
SD	14.09574	0.493379

1. Now we test that claim that IQ mean of 100 at 95% Confidence level

sample size, n = 25

z = (100-114.24)/14.09

= -1

For this z, p = 0.16

0.16>0.05

Hence IQ mean is100 at 95% Confidence level

2. Now, we test that majority students have GPA>3

H0: GPA<=3

H1: GPA>3

z = (3-3.3)/0.49 = 0.6

Hence, from z tabbe, p = 0.27 which is greater than 0.05

Hence we accept null hypothesis.

So, majority students doesn't have GPA >3

3.Now checking at 98% Confidence level

our critical p value will be 0.02 instead of 0.05 as in previous case

Still 0.27>0.02

Hence mean students doesn't have GPA >3 at 98% Confidence level

4. SD(IQ score) = 14.09

There is no Confidence level provided. Hence we can't test whether IQ standard deviation is 15.

Our calculated SD is 14.09 which isn't equal to 15