Question

Assume that the weights of spawning Chinook salmon in the Columbia River are normally distributed with a population standard deviation (σ) of 3.9 pounds. You randomly catch and weigh 20 such salmon. The mean weight from your sample is 24.9 pounds. Test the claim that the mean weight of Columbia River salmon is greater than 24 pounds. Use a 0.10significance level.

(a) What type of test is this?

This is a right-tailed test.

This is a left-tailed test.     

This is a two-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
z_x=  

(c) What is the P-value of the test statistic? Round your answer to 4 decimal places.
P-value =  

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀     

(e) Choose the appropriate concluding statement.

The data supports the claim that the mean salmon weight in the Columbia River is greater than 24 pounds.

There is not enough data to support the claim that the mean salmon weight in the Columbia River is greater than 24 pounds.     

We reject the claim that the mean salmon weight in the Columbia River is greater than 24 pounds.

We have proven that the mean salmon weight in the Columbia River is greater than 24 pounds.

Answer 1

The statistical software output for this problem is :

This is a right-tailed test.

Test statistics = 1.03

P-value = 0.1510

fail to reject H₀     

There is not enough data to support the claim that the mean salmon weight in the Columbia River is greater than 24 pounds.