Resources:

Test-for-the-mean_Population-variance-known.xlsx

Step 1: Defining the Sample Data

For a single sample with known variance:

• We are testing whether the average data scientist salary is truly $113,000.

• We have sample data (source: glassdoor.com):

  • Sample mean (Xˉ) = $100,200
  • Population standard deviation (σ) = $15,000
  • Sample size (n) = 30

• The population variance is known, so we use the Z-test.

• We are conducting a two-tailed test (because we are interested in whether the salary is significantly lower OR higher than $113,000).

Step 2: Setting Up Hypotheses

• Null Hypothesis (H0): The true population mean salary is $113,000.

  H0:μ=113,000

• Alternative Hypothesis (HA): The true population mean salary is not $113,000.

  HA:μ≠113,000