SOLUTION: A researcher was interested in comparing the GPAs of students at two different colleges. Independent random samples of 25 students from college A and 40 students from college B wer

Question 1196774: A researcher was interested in comparing the GPAs of students at two different colleges. Independent random samples of 25 students from college A and 40 students from college B were selected, and all the GPAs for these selected students were collected. The summary statistics are shown below. Do the data provide enough evidence to show that the mean GPA of students at college A is different from the mean GPA of students at college B? What's the difference between population means for the GPAs?
College A x1=3.1124, s1=0.4357, n1=25
College B x2=3.4385, s2=0.5485, n2=40

Using hypothesis testing at a 5% significance level, what would be the formal conclusion?

Accept the Ho.

Reject Ho in favor of HA.

Fail to reject the Ho.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i put the data into the two sample t-test calculator at https://www.statskingdom.com/140MeanT2eq.html.
it determined that the results were significant at the 5% two tailed significance level.
consequently, H0 is rejected in favor of Ha.
here are the results from using that calculator.

the absolute value of difference between the means of each group is equal to 3.4385 - 3.1124 = .3261
the t-test tutorial at https://www.statology.org/two-sample-t-test/ provides the step used to generate these results.
i used it to confirm that the answer from the calculator was consistent with the steps provided through the tutorial.
it was.
i also used a simpler two sample t-test calculator at https://www.inchcalculator.com/t-test-calculator/.
the results from this calculator were consistent with the results i calculated manually and through the other calculator.

RELATED QUESTIONS
Test the indicated claim about the means of two populations and find confidence interval. (answered by Boreal)

A university admitted 100 students who transferred from other institutions. Of these... (answered by stanbon)

A smartphone company is interested in comparing the quality of work at two of its... (answered by Boreal)

A university admitted 100 students who transferred from other institutions. Of these... (answered by scott8148)

1. The mean serum cholesterol level in a certain population of normal healthy men is 240 (answered by math_tutor2020,ikleyn)

A researcher is investigating which of the two newly developed automobile engine oil is... (answered by robertb)

A telephone company estimate that 30% of its customers are interested in high speed... (answered by reviewermath)

In 2005, there were 11,500 students at college A, with a projected enrollment increase of (answered by lwsshak3)

a researcher was interested to study variations in number of deaths from two types of... (answered by mathmate)