Question

The sample consisted of 50 night students, with a sample mean GPA of 3.02 and a standard deviation of 0.08, and 25 day students, with a sample mean GPA of 3.04 and a standard deviation of 0.06. The test statistic is:

Answer 1

Answer: The test statistic is t= -0.90.

Explanation:

Since we have given that

n₁ = 50

n₂ = 25

`\bar{x_1}=3.02\\\\\bar{x_2}=3.04\\\\\sigma_1=0.08\\\\\sigma_2=0.06`

So, s would be

`s=\sqrt{(n_1\sigma_1^2+n_2\sigma_2^2)/(n_1+n_2-2)}\\\\s=\sqrt{(50* 0.08^2+25* 0.06^2)/(50+25-2)}\\\\s=0.075`

So, the value of test statistic would be

`t=\frac{\bar{x_1}-\bar{x_2}}{s((1)/(n_1)+(1)/(n_2))}\\t=(3.02-3.04)/(0.074((1)/(50)+(1)/(25)))\\\\t=(-0.04)/(0.074(0.02+0.04))\\\\t=(-0.04)/(0.044)\\\\t=-0.90`

Hence, the test statistic is t= -0.90.