Question

In: Statistics and Probability

Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally...



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 28.2 pounds with a standard deviation of 4.4 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 25 pounds and why?

No, because 25 is above the lower limit of the confidence interval.Yes, because 25 is below the lower limit of the confidence interval.     No, because 25 is below the lower limit of the confidence interval.Yes, because 25 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 we do not know the distribution of the parent population.     Because the parent population is assumed to be normally distributed.Because the sample size is greater than 10.

Solutions

Expert Solution

Solution :

Given that,

a) Point estimate = sample mean = = 28.2

sample standard deviation = s = 4.4

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 =24

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,24 = 1.711

Margin of error = E = t/2,df * (s /n)

= 1.711 * ( 4.4/ 25)

Margin of error = E = 1.506

The 90% confidence interval estimate of the population mean is,

- E < < + E

28.2 - 1.506 < < 28.2 + 1.506

( 26.694 < < 29.706 )

Yes, because 25 is above the lower limit of the confidence interval

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

Please like if it helps me

Thank you so much.....


Related Solutions

Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally...
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 4.6 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...
Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally...
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...
Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally...
Salmon Weights: 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 4.8 pounds. We 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...
Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally...
Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You randomly catch and weigh 17 such salmon. The mean weight from your sample is 22.2 pounds with a standard deviation of 4.4 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...
Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally...
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...
Salmon Weights: Assume that the weights of spawning Chinook salmon in the Columbia river are normally...
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 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...
Assume that the weights of spawning Chinook salmon in the Columbia river are normally distributed. You...
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 19.2 pounds with a standard deviation of 4.4 pounds. We 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...
Salmon: Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You...
Salmon: Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You randomly catch and weigh 25 such salmon. The mean weight from your sample is 24.1 pounds with a standard deviation of 2.5 pounds. Test the claim that the mean weight of Columbia River salmon is greater than 23 pounds. Test this claim at the 0.05 significance level. (a) What type of test is this? This is a left-tailed test. This is a right-tailed test.  ...
almon: Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You...
almon: Assume that the weights of Chinook Salmon in the Columbia River are normally distributed. You randomly catch and weigh 25 such salmon. The mean weight from your sample is 23.7 pounds with a standard deviation of 3.5 pounds. Test the claim that the mean weight of Columbia River salmon is greater than 23 pounds. Test this claim at the 0.05 significance level. (a) What type of test is this? This is a left-tailed test. This is a two-tailed test....
Salmon (Raw Data, Software Required): Assume that the weights of Chinook Salmon in the Columbia River...
Salmon (Raw Data, Software Required): Assume that the weights of 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. Test the claim that the mean weight of Columbia River salmon is greater than 27 pounds. Test this claim at the 0.10 significance level. (a) What type of test is this? This is a two-tailed test.This is a left-tailed test.     This is a right-tailed test. (b)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT