Question

The difference in the mean sleep hours between two groups of students (Freshmen and upperclassmen).

What could the study design and type in this sentence be?

Answer 1

To study the difference in two population mean , that is to see if two population means are equal

For this we use either two sample z test or two sample t test ( unpaired)

If the two sample size is large and population variances are known then we use z test

If the population variances are not known we use t test

For this test the null hypothesis is

The alternative hypothesis are one of them

Test statistic for z test

where and are sample means and population standard deviation

Test statistic for t test

where is the pooled standard deviation

here si are sample standard deviations

then we find the p value or compare the test statistic with critical value to come to the conclusion whether there is significant difference between population means