Question

Provided below are summary statistics for independent simple random samples from two populations. Preliminary data analyses indicate that the variable under consideration is normally distributed on each population. Decide whether use of the pooled​ t-test and pooled​ t-interval procedure is reasonable. x overbar 1equals485.6​, s 1equals44.3​, n 1equals49​, x overbar 2equals390.1​, s 2equals61.3​, n 2equals31.

Is use of the pooled t-test and pooled t-interval procedure reasonable or not reasonable?

A. Reasonable

B. Not reasonable

Answer 1

Answer:

Not reasonable.

Step-by-step explanation:

Hello!

You have two samples from normally distributed variables. Let's say:

Sample 1

X[bar]₁= 485.6

S₁= 44.3

n₁= 49

Sample 2

X[bar]₂= 390.1

S₂= 61.3

n₂= 31

A Student-t distribution is graphically almost identical to a normal distribution. This distribution is defined as:

$T= \frac{Z}{\sqrt{V} }$

Where Z is variable with normal distribution and V is a variable with chi-square distribution and Z and V are independent variables.

This is the reason why the distribution looks so much like a normal distribution and, as the sample sizes grow, it tends to be identical to the normal distribution.

Depending on the criteria of the statistics course you are taking, it is the sample size from which you stop choosing to use the student's t and you start using the normal distribution. In general, with n greater than 20 or 30 the normal approximation is already used.

Applying these criteria, since n₁ and n₂ are bigger than 30 I wouldn't recommend using the pooled t-test.

I hope it helps!