Question

Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You randomly catch and weigh 25 such salmon. The mean weight from your sample is 31.2 pounds with a standard deviation of 4.6 pounds. You want to construct a 90% 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 90% 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 90% confident that the mean weight of all spawning Chinook salmon in the Columbia River is greater than 28 pounds and why?

No, because 28 is above the lower limit of the confidence interval.

Yes, because 28 is below the lower limit of the confidence interval.

No, because 28 is below the lower limit of the confidence interval.

Yes, because 28 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 greater than 10.

Because the parent population is assumed to be normally distributed.

Because the sample size is less than 100.

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

Answer 1

a) The point estimate of the mean weight for all spawning chinook salmon is given as the sample mean which is given to be 31.2 pounds here. Therefore 31.2 is the point estimate required here.

b) From standard normal tables, we have here:
P( -1.645 < Z < 1.645) = 0.9

Therefore the 90% confidence interval here is obtained as:

This is the required confidence interval here.

c) As the whole confidence interval lies above 28 which means that the lower limit of the confidence interval is greater than 28, therefore Yes we are 90% confidence that the mean is greater than 28 here.

Therefore D is the correct answer here.

d) We are given here that the underlying distribution is normal and so we dont need the sample size condition here to apply the central limit theorem. Therefore the correct reason here is given as: Because the parent population is assumed to be normally distributed.