Question

The weights of four randomly and independently selected bags of tomatoes labeled 5.0 pounds were found to be 5.1​, 5.0​, 5.1​, and 5.2 pounds. Assume Normality. Answer parts​ (a) and​ (b) below.

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

Answer 1

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 5.1

S = 0.081649658

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 = 5.1 ± 3.1824*0.081649658/sqrt(4)

Confidence interval = 5.1 ± 0.1299

Lower limit = 5.1 - 0.1299 = 4.97

Upper limit = 5.1 + 0.1299 = 5.23

Confidence interval = (4.97, 5.23)