Question

Salmon (Raw Data, Software Required):
Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You randomly catch and weigh 15 such salmon. The data is found in the table below. Test the claim that the mean weight of Columbia River salmon is greater than 26 pounds. Test this claim at the 0.05 significance level.

(a) What type of test is this? This is a left-tailed test.This is a two-tailed test.    This is a right-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 H0fail 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 26 pounds.There is not enough data to support the claim that the mean weight of Columbia River salmon is greater than 26 pounds.    We reject the claim that the mean weight of Columbia River salmon is greater than 26 pounds.We have proven that the mean weight of Columbia River salmon is greater than 26 pounds.

DATA ( n = 15 ) Salmon Weights Pounds    25.7 24.8 36.0 26.6 18.9 22.5 33.2 25.8 23.5 26.8 32.5 27.7 28.8 28.3 31.5

Answer 1

a. Here claim is that the mean weight of Columbia River salmon is greater than 26 pounds

So hypothesis is vs

Hence it is right tailed test

b. For given sample mean is

Create the following table.

data	data-mean	(data - mean)2
25.7	-1.8067	3.26416489
24.8	-2.7067	7.32622489
36.0	8.4933	72.13614489
26.6	-0.9067	0.82210488999999
18.9	-8.6067	74.07528489
22.5	-5.0067	25.06704489
33.2	5.6933	32.41366489
25.8	-1.7067	2.91282489
23.5	-4.0067	16.05364489
26.8	-0.7067	0.49942489
32.5	4.9933	24.93304489
27.7	0.1933	0.03736489
28.8	1.2933	1.67262489
28.3	0.7933	0.62932489
31.5	3.9933	15.94644489

Find the sum of numbers in the last column to get.

So

b. So test statistics is

c. P value is TDIST(1.31,14,1)=0.1056

d. As P value is greater than alpha=0.05, we fail to reject the null hypothesis

e. Hence we do not have sufficient evidence to support the claim that mean is greater than 26.

There is not enough data to support the claim that the mean weight of Columbia River salmon is greater than 26 pounds.