Wyoming fisheries contend that the mean number of cutthroat trout caught during a full day of fly-fishing on the Snake, Buffalo, and other rivers and streams in the Jackson Hole area is 4.0. To make their yearly update, the fishery personal asked a sample of fly-fishermen to keep a count of the number caught during the day. The numbers were: 4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6. At the 0.05 significance level, can we conclude that the mean number caught is greater than 4.0?

The degrees of freedom are given by:

And the p value would be:

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4

Step-by-step explanation:

We have the following data given:

4, 4, 3, 2, 6, 8, 7, 1,9, 3, 1, and 6

The sample mean and deviation from these data are:

represent the sample mean  

represent the sample deviation

sample size  

represent the value to verify

represent the significance level

t would represent the statistic

represent the p value

Hypothesis to verify

We want to verify if the true mean is equal to 4, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Replacing the the info we got:

The degrees of freedom are given by:

And the p value would be:

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean area is not significantly different from 4

0.0076, if you meant 4.125 divided by 0.03125 it would be 132

step-by-step explanation:

first you have to move the decimal in 0.03125 over until its behind the 5 which is 5 places over. now the number is 3125

then you have to move the decimal in 4.125, 5 places over. now the number is 4,112,500.

now you divide like you would normally would and get 0.0076