Question

Test the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.2 significance level.

The null and alternative hypothesis would be:

H0:pN=pD

H1:pN<pD

H0:pN=pD

H1:pN≠pD

H0:pN=pD

H1:pN>pD

H0:μN=μD

H1:μN≠μD

H0:μN=μD

H1:μN<μD

H0:μN=μD

H1:μN>μD

The test is:

two-tailed

right-tailed

left-tailed

The sample consisted of 25 night students, with a sample mean GPA of 2.01 and a standard deviation of 0.08, and 60 day students, with a sample mean GPA of 1.96 and a standard deviation of 0.05.

The test statistic is: (to 2 decimals)

The positive critical value is: (to 2 decimals)

Based on this we:

• Fail to reject the null hypothesis
• Reject the null hypothesis

I do not need to know how to do the problem by hand. I need to know how to do it on a ti-84 calculator which I'm not sure how.

Answer 1

Answer 1

it is given that we have to test whether the mean GPA of night students is significantly different than the mean GPA of day students

Here word "different" shows that it is a two tailed hypothesis test for means

H0:μN=μD
H1:μN≠μD

Test is tailed

Using TI 84 calculator

press stat then tests then select 2-sampTtest

enter the data

x1 = 2.01, s1 = 0.08, n1 = 25

x2 = 1.96, s2= 0.05, n2 = 60

Pooled: No

press calculate

we get

test statistc = 2.90

t critical = T.INV.2T(alpha,df)

where degree of freedom (df) = 32 (using TI 84 result) and alpha = 0.2

t critical = T.INV.2T(0.2,32) = 1.31

Reject null hypothesis as the test statistic is greater than t critical value