Question

The data below comes from a university that wanted to see if there was a relationship between IQ scores and the GPA’s of students after their freshman year. Please provide the claim, critical values, test statistic and conclusion. If answered correctly will leave a like.

GPA 3.68 3.10 2.72 3.61 4.0 3.89 3.51 2.64 3.33 3.32 2.91 3.81 3.53 3.95 3.57 3.22 IQ 126 105 104 118 126 154 118 98 108 108 95 113 128 134 116 103 119 104 100 116 3 4.0 2.32 2.65 3.42 3.55 2.94 2.75 2.6 3.56 123 95 105 107 133 5) Divide the data into two groups: those with under a 110 IQ and those with at least 110 IQ. a) Test the claim that the mean GPA is 3.0 for those with under a 110 IQ. For each hypothesis test, provide the claim, critical values, test statistic and conclusion. 5) Divide the data into two groups: those with under a 110 IQ and those with at least 110IQ. b) Test the claim that the mean GPA is 3.0 for those with at least 110 IQ. For each hypothesis test, provide the claim, critical values, test statistic and conclusion.

Answer 1

Answer:

The data below comes from a university that wanted to see if there was a relationship between IQ scores and the GPA’s of students after their freshman year. Please provide the claim, critical values, test statistic and conclusion. If answered correctly will leave a like.

Sorted data:

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

5a).

Ho : μ = 3.0 H1 : μメ3.0

(z-1)

(2.875 - 3) 12

=-1.3636              

Table value of t with 11 DF at 0.05 level =2.201

Rejection Region: Reject Ho if t < -2.201 or t > 2.201

Calculated t =-1.3636 not in the rejection region

The null hypothesis is not rejected.

There is not enough evidence to reject the claim of GPA is 3.0

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	3
Level of Significance	0.05
Sample Size	12
Sample Mean	2.875
Sample Standard Deviation	0.3176
Intermediate Calculations
Standard Error of the Mean	0.0917
Degrees of Freedom	11
t Test Statistic	-1.3636
Two-Tail Test
Lower Critical Value	-2.2010
Upper Critical Value	2.2010
p-Value	0.2000
Do not reject the null hypothesis

5b).

Ho : μ = 3.0 H1 : μメ3.0

-3) (3.6985 0.2044

=12.3180

Table value of t with 12 DF at 0.05 level =2.1788

Rejection Region: Reject Ho if t < -2.1788 or t > 2.1788

Calculated t =12.3180 falls in the rejection region

The null hypothesis is rejected.

There is enough evidence to reject the claim of GPA is 3.0

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	3
Level of Significance	0.05
Sample Size	13
Sample Mean	3.6985
Sample Standard Deviation	0.2044
Intermediate Calculations
Standard Error of the Mean	0.0567
Degrees of Freedom	12
t Test Statistic	12.3180
Two-Tail Test
Lower Critical Value	-2.1788
Upper Critical Value	2.1788
p-Value	0.0000
Reject the null hypothesis