Question

a. Test the claim that the mean GPA of night students is significantly different than 3.2 at the 0.05 significance level. The null and alternative hypothesis would be:

Null Hypothesis: mu = 3.2

Alternative Hypothesis: mu ≠ 3.2

The test is: two-tailed

Based on a sample of 40 people, the sample mean GPA was 3.18 with a standard deviation of 0.04

The test statistic is: _____(to 2 decimals)

The positive critical value is:______ (to 2 decimals)

b. Test the claim that the mean GPA of night students is smaller than 3.2 at the 0.10 significance level.

The null and alternative hypotheses would be:

H0:μ=3.2
H1:μ<3.2

The test is:

left-tailed

Based on a sample of 37 people, the sample mean GPA was 3.19 with a standard deviation of 0.1

The p-value is: _____(to 3 decimals)

The significance level is: ______(to 2 decimals)

Answer 1

a)

population mean μ=		3.2
sample mean 'x̄=		3.180
sample size    n=		40
std deviation s=		0.0400
std error ='sx=s/√n=0.04/√40=		0.0063
test statistic t='(x̄-μ)/sx=(3.18-3.2)/0.006=		-3.16

0.05 level with two tail test and n-1= 39 df, critical t=

2.02

b)

population mean μ=		3.2
sample mean 'x̄=		3.190
sample size    n=		37
std deviation s=		0.1000
std error ='sx=s/√n=0.1/√37=		0.0164
t statistic ='(x̄-μ)/sx=(3.19-3.2)/0.016=		-0.608
p value      =		0.273		from excel: tdist(0.608,36,1)

the significance level is 0.10