Question

The supervisor of a fish hatchery measures the length of a particular species every week after hatching to track their growth. If their average length is too short or too long, they are not maturing properly and further tests must be done to determine the cause. She randomly selects 30 fish from among those that hatched five weeks ago and measures their individual lengths in inches to determine if they have grown to an average length of 9.7 inches. She observes an average length of 10.1 inches among the sample. What set of hypotheses is she interested in testing

Answer 1

The z-test score is used for this hypothesis test to decide whether to reject or not to reject the null hypothesis. The z-test score for the given sample is 1.22.

How to calculate z-score for the hypothesis test?

The z-score for the hypothesis test is calculated by,

z-score = (X - μ)/(σ/√n)

Where X - sample mean, μ - population mean, σ - standard deviation, and n - sample size.

Calculation:

It is given  that,

Sample size n = 30

Population mean μ = 9.7

Sample mean X = 10.1

Standard deviation σ = 1.8

So, the z-score is

= (10.1 - 9.7)/(1.8/√30)

= 0.4/0.328

= 1.219 ≅ 1.22

Therefore, the p-value for this z-score is 0.22. This value decides whether to reject or not to reject the null hypothesis.

Learn more about hypothesis testing here:

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