Consider the following hypothesis test: H0: μ1 - μ2 = 0 Ha: μ1 - μ2 ≠ 0 There are two independent samples taken from the two populations: Sample 1 Sample 2 n1 = 81 n2 = 64 Sample average = 110 Sample average = 108 Population standard deviation = 7.2 Population standard deviation = 6.3 ​ What is the value of the test statistic.

The value of the test statistic is

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Sample 1:

Sample 2:

The test statistic is:

In which X is the sample mean, is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that

Distribution of the difference:

What is the value of the test statistic?

The value of the test statistic is

three-fourths of an hour

36÷48=0.75

0.75=