Question

2. It had always been thought that the mean length for a great white shark was 22 feet. Nine great whites caught off the coast of Australia averaged 24 feet with a standard deviation of 3 feet.

a) Which hypotheses would you use to test the theory that the mean length of great white sharks off the coast of Australia are longer than great white sharks caught elsewhere?

b) A sample of 9 great white sharks caught off the coast of Australia averaged 24 feet with a standard deviation of 3 feet. What assumptions do you need in order to use this test statistic? Compute a test statistic under H₀.

Assumptions:

Test statistic:

c) Compute the p-value. With α=.05, do you reject or not H₀. Make a conclusion in terms of the researcher’s research interest.

Answer 1

a)

Here, we use single mean hypothesis test

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 22
Alternative Hypothesis, Ha: μ < 22

b)

assumptions:

• In theory, the data should be drawn from a normal distribution or it is a large sample (need
to check that n ≥ 30 ). .
• The data must be reasonably random.
• The sample must be less than 10% of the population.

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (24 - 22)/(3/sqrt(9))
t = 2

c)

P-value = 0.9597
As P-value >= 0.05, fail to reject null hypothesis.