Question

Emma, a golfer, claims that her drive distance is less than 175 meters, on average. Several of her friends do not believe her, so she decides to do a hypothesis test, at a 1% significance level, to persuade them. She hits 17 drives. The mean distance of the sample drives is 156 meters. Emma knows from experience that the standard deviation for her drive distance is 19 meters. H₀: μ ≥ 175; Ha: μ < 175 α = 0.01 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Answer 1

The test statistic (z-score) for this one-mean hypothesis test is approximately -3.18.

Step-by-step explanation:

In order to find the test statistic (z-score) for this one-mean hypothesis test, we can use the formula:

z = (x - μ) / (σ / √n)

Where:

• z is the test statistic
• x is the sample mean
• μ is the population mean
• σ is the population standard deviation
• n is the sample size

Substituting the given values into the formula:

z = (156 - 175) / (19 / √17) ≈ -3.18

Therefore, the test statistic (z-score) of this one-mean hypothesis test is approximately -3.18.