Question

Consider the following hypothesis test
H₀: μ>=16
Η₁: μ < 16
A sample of 36 provided a sample mean of 15.4. The population standard deviation is 3. The value of the test statistic 't' is.

• A. -2.2
• B. 1.25
• C. -1.2
• D. 1.42

Answer 1

The Correct Option is C

To solve this hypothesis testing problem, we need to calculate the test statistic for the given data. The hypothesis we have is a one-tailed test:
H₀: μ≥16 (null hypothesis)
H₁: μ<16 (alternative hypothesis)

Given data:
Sample size (n) = 36
Sample mean (x̄) = 15.4
Population standard deviation (σ) = 3
Population mean under H₀ (μ) = 16

The formula for the z-test statistic is:

z = (x̄ − μ) / (σ/√n)

Substituting the given values into the formula:

z = (15.4 − 16) / (3/√36)

z = (−0.6) / (3/6)

z = (−0.6) / 0.5

z = −1.2

Thus, the calculated test statistic is −1.2, which matches the correct answer from the provided options.