Question

Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You randomly catch and weigh 18 such salmon. The mean weight from your sample is 22.2 pounds with a standard deviation of 4.7 pounds. You want to construct a 99% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River.

(a) What is the point estimate for the mean weight of all spawning Chinook salmon in the Columbia River?
pounds =

(b) Construct the 99% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. Round your answers to 1 decimal place.
? < μ < ?

(c) Are you 99% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 20 pounds and why?

No, because 20 is above the lower limit of the confidence interval.

Yes, because 20 is below the lower limit of the confidence interval.     

No, because 20 is below the lower limit of the confidence interval.

Yes, because 20 is above the lower limit of the confidence interval.

(d) Recognizing the sample size is less than 30, why could we use the above method to find the confidence interval?

Because the sample size is less than 100.

Because the sample size is greater than 10.  

   Because the parent population is assumed to be normally distributed.

Because we do not know the distribution of the parent population.

Answer 1

(a) What is the point estimate for the mean weight of all spawning Chinook salmon in the Columbia River?
It is same as the sample mean = 22.2 pounds.

Here population standard deviation is not given and we use sample standard deviation(s) instead of population standard deviation ( ). Also we assume that the sample comes from normal population. So we can used one sample t confidence interval for population mean( )

Using minitab:

Step 1) Click on Stat>>>Basic Statistics >>1 sample t...

Select summarized data

Sample size: 18

Mean: 22.2

Standard deviation: 4.7

Step 2) Click on Option

Confidence level = 99

Alternative: Not equal

Then click on OK

Again Click on OK

Then we get the following output

From the above output, we get

(b) Construct the 99% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. Round your answers to 1 decimal place.
19.0 < μ < 25.4

(c) Are you 99% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 20 pounds and why?

The correct choice is as "No, because 20 is above the lower limit of the confidence interval."

(d) Recognizing the sample size is less than 30, why could we use the above method to find the confidence interval?

The correct choice is as " Because the parent population is assumed to be normally distributed."