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 *H*_{0} fail to reject
*H*_{0}

(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
H_{0} **

(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.**

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