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 0.01 significance level.

(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 = ?

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

here, as the population sd is unknown , we will do 1 sample t test for mean.

hypothesis:-

necessary calculations:-

Pounds()
25.7	3.264165
24.8	7.326225
36	72.13614
26.6	0.822105
18.9	74.07528
22.5	25.06704
33.2	32.41366
25.8	2.912825
23.5	16.05364
26.8	0.499425
32.5	24.93304
27.7	0.037365
28.8	1.672625
28.3	0.629325
31.5	15.94644
sum= 412.6	sum = 277.789

sample size (n) = 15

test statistic be:-

degrees of freedom = (n-1) = (15-1) = 14

p value = 0.1056

[ using software for, t = 1.31, df = 14, one tailed test ]

decision:-

p value = 0.1056 >0.01 ()

so, we do not have enough evidence to reject the null hypothesis.

conclusion:-

there is not sufficient evidence to support the claim that the mean weight of Columbia River salmon is greater than 26 pounds at 0.01 level of significance.

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