Question

Hi, can you help me answer this question please, thank you!

Answer 1

Given data:

Data are normally distibuted. Unknown standard deviation but variances are assumed to be equal.

FIrst Population Data

Sample size (n₁) = 12

Sample mean (x₁) = 75.4

Sample SD (s₁) = 9.7

Second Population Data

Sample size (n₂) = 19

Sample Mean (x₂) = 83.3

Sample SD (s₂) = 17.8

Find: test statistic value and p-value

Solution:

Since both population have small sample size (less than 30) and the population standard deviation is unknown as well, the appropriate test statistic that must be use is the t-test. Here is the formula:

`t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt[]{((n_1-1)(s^2_1)+(n_2-1)(s^2_2))/(n_1+n_2-2)((1)/(n_1)+(1)/(n_2))}};df=n_1+n_2-2`

Let's plug those given data that we have above to the formula.

`t=\frac{75.4-83.3}{\sqrt[]{((12-1)(9.7^2)+(19-1)(17.8)^2)/(12+19-1)((1)/(12)+(1)/(19))}}`