Question

Salmon: Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You randomly catch and weigh 30 such salmon. The mean weight from your sample is 23.8 pounds with a standard deviation of 2.5 pounds. Test the claim that the mean weight of Columbia River salmon is greater than 23 pounds. Test this claim at the 0.01 significance 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.
t

_x

=

(c) Use software to get the P-value of the test statistic. Round 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 weight of Columbia River salmon is greater than 23 pounds. There is not enough data to support the claim that the mean weight of Columbia River salmon is greater than 23 pounds.     We reject the claim that the mean weight of Columbia River salmon is greater than 23 pounds. We have proven that the mean weight of Columbia River salmon is greater than 23 pounds.

Answer 1

Solution-A:

Ho:mu=23

Ha:mu>23

This is a right-tailed test

Solution-B:

t=xbar-mu/s/sqrt(n)

=(23.8-23)/(2.5/sqrt(30))

t=1.75

test statistic,t=1.75

Solution-c:

test statistic=1.75

df=n-1=30-1=29

p value is

=T.DIST.RT(1.75;29)

=0.045347012

p=0.0453

Solutiond:

p=0.0453

p>0.01

Fail to reject Ho.

fail to reject H₀    

(e) Choose the appropriate concluding statement.

There is not enough data to support the claim that the mean weight of Columbia River salmon is greater than 23 pounds.