MAT*H167: Principles of Statistics

Quiz 12

Please answer the following questions and attach your work to the submission link in Blackboard.

The attached spreadsheet contains data on the year, experience level, and salary in U.S. dollars for random samples of 79 entry-level and 206 mid-level data science jobs from 2020-2022.

Suppose that you would like to know if the mean salary for all mid-level data science jobs is greater than the mean salary for all entry-level data science jobs.

1. [4] Describe the two samples selected.

2. [4] Describe the two populations of interest.

3. [4] Describe the two parameters of interest.

4. [10] What null and alternative hypotheses should you test regarding the two parameters of interest?

5. [4+4] List the four conditions the data must satisfy in order for us to be able to compute a confidence interval AND briefly explain why each condition is satisfied.

6. [5] What is the value of the test statistic?

7. [5] What is the P-value?

8. [4] Should you reject the null hypothesis in favor of the alternative or fail to reject the null hypothesis in favor of the alternative? Test at the 0.05 significance level.

9. [2+2] Is there significant evidence to support the claim that the mean salary for all mid-level data science jobs is greater than the mean salary for all entry-level data science jobs? Explain your reasoning below.