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In: Statistics and Probability

A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed...

A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 9.6, 9.3, 9.1,and.9.1 pounds.

Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges.

Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds?

Yes, it does capture 10. Reject the claim of 10 pounds because 10 is in the interval.

?No, it does not capture 10. Reject the claim of 10 pounds because 10 is not in the interval.

?Yes, it does capture 10. Do not reject the claim of 10 pounds because 10 is in the interval.

?No, it does not capture 10. Do not reject the claim of 10 pounds because 10 is not in the interval.

Solutions

Expert Solution

Solution: Find a 95% confidence interval for the mean weight of all bags of oranges.

Answer: The 95% confidence interval for the mean weight of all bags of oranges is given below:

Where

is the t critical value at 0.05 significance level for and is given below:

is the sample standard deviation and is given below:

Therefore, 95% confidence interval for the mean weight of all bags of oranges is

Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds?

Answer: ?No, it does not capture 10. Reject the claim of 10 pounds because 10 is not in the interval.

  

orchestra answered 2 years ago
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