Question

An Independent Samples T Test is used to make an inference about whether two groups in the population have different averages on some quantitative measure or dependent variable. This test could be used to compare the average annual earnings of High School graduates, compared to Community College graduates For this potential research question, answer the following questions. Please use only numeric values in your answers to questions 1, 2 and 3 and a word to answer question 4 1) According to the Null Hypothesis, the difference in earnings would be 2) With an alpha of.05, and 2,000 cases, what would the critical value of t be? 3) What is the risk of Type 1 error in this test? 4) If the Alternative Hypothesis is that Community College graduates earn more than High School graduates, is this hypothesis directional or non-directional?

Answer 1

1)   

Average annual earnings of High School graduates = $\mu$₁ (let)

Average annual earnings of Community College graduates = $\mu$₂ (let)

Null Hypothesis H₀ : $\mu$₁ - $\mu$₂ = 0

2)   

Size of sample from High School graduates = n₁ (let)

Size of sample from Community College graduates = n₂ (let)

$t-statistic\sim t_{n_{1}+n_{2}-2}$

Given n₁ = 2000 , n₂ = 2000 , $\alpha$ = 0.05

For the alternate hypothesis $\mu$₁ < $\mu$₂ in question 4 ;

$Critical\;value=-t_{\alpha;n_{1}&plus;n_{2}-2}=-t_{0.05;3998}=-1.645$

3)   

The risk of Type 1 error is the probability of rejecting the null hypothesis according to the data obtained from the sample although null hypothesis is true; which is equal to the level of significance of the test.

Risk of Type 1 error = P(Type 1 error) = $\alpha$ = 0.05

4)   

Alternate hypothesis H₁ ; $\mu$₁ < $\mu$₂

This hypothesis is directional, as it assumes a relationship between the average annual earnings of High School graduates and Community College graduates. This test is one-tailed test.