Question

Assume that you have a sample of n 1 equals 8​, with the sample mean Upper X overbar 1 equals 42​, and a sample standard deviation of Upper S 1 equals 4​, and you have an independent sample of n 2 equals 15 from another population with a sample mean of Upper X overbar 2 equals 34 and a sample standard deviation of Upper S 2 equals 5. What assumptions about the two populations are necessary in order to perform the​ pooled-variance t test for the hypothesis Upper H 0 : mu 1 equals mu 2 against the alternative Upper H 1 : mu 1 greater than mu 2 and make a statistical​ decision?

Answer 1

Solution: The assumptions that are necessary in order to perform the pooled-variance t-test are:

1. The two population from which the samples are taken have the same variance

2. The two populations are normally distributed.

3. The two samples taken from these two populations are random and independent of each other.

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Where:

  

  

Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that the mean of the first population is greater than the mean of the second population.