Question

Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You randomly catch and weigh 40 such salmon. The mean weight from your sample is 23.6 pounds with a standard deviation of 3.5 pounds. Test the claim that the mean weight of Columbia River salmon is greater than 23 pounds. Test this claim at the 0.10 significance level.

(a) What type of test is this?i) This is a right-tailed test.ii) This is a two-tailed test. iii) This is a left-tailed test.(b) What is the test statistic? Round your answer to 2 decimal places.

Answer 1

a) i) This is a right-tailed test.

b)

`\text{Test statistic} = 1.08`

Explanation:

We are given the following in the question:

Population mean, μ = 23 pounds

Sample mean,
`\bar{x}` = 23.6 pounds

Sample size, n = 40

Alpha, α = 0.10

Sample standard deviation, s = 3.5 pounds

First, we design the null and the alternate hypothesis

`H_(0): \mu = 23\text{ pounds}\\H_A: \mu > 23\text{ pounds}`

This is a one tailed(right).

Formula:

`\text{Test statistic} = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n)) }`

Putting all the values, we have

`\text{Test statistic} = \displaystyle(23.6 - 23)/((3.5)/(√(40)) ) = 1.08`