Question

The weights of four randomly and independently selected bags of potatoes labeled 20.0 pounds were found...

The weights of four randomly and independently selected bags of potatoes labeled 20.0 pounds were found to be 20.6, 21.4​, 20.9, and 21.2 pounds. Assume Normality. Answer parts​ (a) and​ (b) below.

a. Find a 95% confidence interval for the mean weight of all bags of potatoes

(___ , ____)

b. Can you reject the population mean of 20 pounds?

Homework Answers

Answer #1

Part a

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 21.025

S = 0.35

n = 4

df = n – 1 = 3

Confidence level = 95%

Critical t value = 3.1824

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 21.025 ± 3.1824*0.35/sqrt(4)

Confidence interval = 21.025 ± 0.5569

Lower limit = 21.025 - 0.5569 = 20.4681

Upper limit = 21.025 + 0.5569 = 21.5819

Confidence interval = (20.4681, 21.5819)

Part b

Yes, we reject the population mean of 20 pounds because the value 20 is not included in the above confidence interval.

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