 Hello, this is a video on two sample hypothesis testing for two means. In my example, we want to test to claim that the mean GPA of night students is smaller than the mean GPA of day students at the 0.10 significance level. The sample consisted of 65 night students with a sample mean GPA of 2.88 and a standard deviation of 0.05 and 65 day students with a sample mean GPA of 2.92 and a standard deviation of 0.08. So group one is going to be my night students and group two is going to be my daytime students. So I'm comparing in my two hypotheses and comparing the mean of night students to the mean of day students. Now, because I called night students group one, that's why the mean of night students is on the left in my hypotheses. Now, the claim is night students mean GPA is smaller than the mean GPA. Since this does not include equality, smaller than or less than goes in the alternative hypothesis. Now, the opposite sign of less than is to say greater than or equal to or in most cases, you would just write equal to. It's just personal preference sometimes. Well, because of my alternative hypothesis having a less than sign, I know that my test is left tailed. Less than is left tailed. Now, let's find the test statistic and the p-value. So the information I want to use for Google Sheets to find the test statistic and p-value would be the sample mean for group one, which in this case is going to be night time students, there are 65 of them. 2.88 was their mean standard deviation was 0.05. So group one, the mean was 2.88 standard deviation of group one would be 0.05 and sample size for group one would be 65. Group two, which is my daytime students. So group one is night, group two would be day. The mean there would be 2.92. The standard deviation is 0.08. And then there are 65 of them, sample size is 65. And my alternative hypothesis in this case had a less than sign. So let's put this information in the Google Sheets. Go to the data list tab. Go to the two variable confidence level p-value region. You'll notice that there's a place to put the mean standard deviation and the sample size for both groups. So starting off with group one, the mean is 2.88. The sample standard deviation is 0.05. Sample size is 65. Group two, 2.92. Sample standard deviation is 0.08 and sample size is 65. Alternative hypothesis, you have less than. So lucky here, we have our test statistic of negative 3.42 and the p-value of 0.0004. So let's put this information on the slide. You have negative 3.42 and the p-value of 0.0004. Let's compare the p-value to alpha. In this case, our significance level or alpha is 0.10. And then I have my p-value. Remember my claim is the alternative hypothesis. The p-value is greater than alpha, so I must fail to reject the null hypothesis. So I fail to reject the null hypothesis. And the original claim does not include equality, so that puts me in row three. My summary statement is there is sufficient evidence to support the claim that the mean GPA of night students is smaller than the mean GPA of day students. Thanks for watching.