Question

QUESTION 6

1. Let x be a random variable representing the length of a cutthroat trout in Pyramid lake. A friend claims that the average length of trout caught in this lake is 19 inches. To test this claim we find that a sample of 13 trout has a mean length of 18.1 inches with a sample standard deviation of 3.3 inches. The population standard deviation is unknown.  If you assume that the population mean is 19, find the P-value corresponding to the hypothesis that the average cutthroat trout length is different from 19 (i.e. two-tail test).

   	A.	0.295
   	B.	0.324
   	C.	0.162
   	D.	0.344

Answer 1

The provided sample mean is 18.1 and the sample standard deviation is s = 3.3 , and the sample size is n = 13

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 19

Ha: μ ≠ 19

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is t_c = 2.179

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

The p-value is p = 0.344