Question

Salmon Weights (Raw Data, Software Required):

Assume that the weights of spawning 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. You want to construct a 99% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. You will need software to answer these questions. You should be able to copy the data directly from the table into your software program.

Salmon    Weight   

1 25.2

2 24.3

3 35.5

4 26.1

5 18.4

6 22.0

7 32.7

8 25.3

9 23.0

10 26.3

11 32.0

12 27.2

13 28.3

14 27.8

15 31.0

(a) What is the point estimate for the mean weight of all spawning Chinook salmon in the Columbia River? Round your answer to 2 decimal places.

pounds

(b) Construct the 99% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River. Round your answers to 2 decimal places.

< μ <   

(c) Are you 99% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 23 pounds and why?

No, because 23 is above the lower limit of the confidence interval.

Yes, because 23 is below the lower limit of the confidence interval.

No, because 23 is below the lower limit of the confidence interval.

Yes, because 23 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 parent population is assumed to be normally distributed.

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

Because the sample size is greater than 10.

Because the sample size is less than 100.

Answer 1