Question

The mean length a particular species of fish should be 9.7 inches. the supervisor of a fish hatchery measures the length of a simple random sample of the fish 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 those hatched five weeks ago and observes a mean length of 10.1 inches and a standard deviation of 1.8 inches. the value of the test statistic is ________. (give the answer rounded to 2 decimal places.)

Answer 1

A test statistic is a parameter used during a hypothesis test to determine whether to accept or reject the null hypothesis. There are 2 test statistics, the z-score and t-score. The main difference is that the t-score is used when sample size is not greater than 30. Therefore we will use the t-score in this case.

The formula for t-score is:

t-score = (x – μ) / (s / sqrt n)               -----> equation 1

Where,

x = sample mean = 10.1

μ = population mean = 9.7

s = sample standard deviation = 1.8

 n = sample size = 30

Substituting the given values in equation 1:

t-score = (10.1 – 9.7) / (1.8 / sqrt(30))

t-score = 1.22

Answer: The test statistic is 1.22.