Answer: t= -0.95
Step-by-step explanation:
Given : You are testing the claim that the mean GPA of night students is greater than the mean GPA of day students.
Let [tex]\mu_1[/tex] and [tex]\mu_2[/tex] are the mean GPA of night students and mean GPA of day students respectively.
Then, Claim : [tex]H_a: \mu_1>\mu_2[/tex]
Test statistic for difference between two population mean :
[tex]t=\dfrac{\overline{x}_1-\overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1}+\dfrac{s_2^2}{n_2}}}[/tex]
, where
[tex]n_1\ \&\ n_2[/tex]= sample standard deviations from population 1 and 2.
[tex]\overline{x}_1-\overline{x}_2[/tex] = difference in two sample means.
[tex]s_1=s_2[/tex]= sample standard deviations from population 1 and 2.
As per given , we have
[tex]\overline{x}_1=2.23\ \&\ \overline{x}_2= 2.33 [/tex]
[tex]n_1=60,\ \ n_2=55[/tex]
[tex]s_1=0.5,\ \ s_2=0.62[/tex]
Test statistic :
[tex]t=\dfrac{2.23-2.33}{\sqrt{\dfrac{(0.5)^2}{60}+\dfrac{(0.62)^2}{55}}}[/tex]
[tex]t=\dfrac{-0.1}{\sqrt{\dfrac{0.25}{60}+\dfrac{0.3844}{55}}}[/tex]
[tex]t=\dfrac{-0.1}{\sqrt{0.0111557575758}}[/tex]
[tex]t=\dfrac{-0.1}{0.1056208198}=-0.946783\approx-0.95[/tex]
Hence, the test statistic : t= -0.95
