Question

Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You randomly catch and weigh 19 such salmon. The mean weight from your sample is 19.2 pounds with a standard deviation of 4.7 pounds. You want to construct a 95% 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 95% 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 95% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 15 pounds and why?

No, because 15 is above the lower limit of the confidence interval.

Yes, because 15 is below the lower limit of the confidence interval.    

No, because 15 is below the lower limit of the confidence interval.

Yes, because 15 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 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.

Because the parent population is assumed to be normally distributed.

Answer 1

Solution:-

a) The point estimate for the mean weight of all spawning Chinook salmon in the Columbia River is 19.2 pounds.

b) 95% confidence interval for the mean weight of all spawning Chinook salmon in the Columbia River is C.I = ( 16.9, 21.5).

C.I = 19.2 + 2.101*1.07825

C.I = 19.2 + 2.2654

C.I = ( 16.935, 21.465)

c) Yes, because 15 is below the lower limit of the confidence interval.   

d) Because the parent population is assumed to be normally distributed.