Question

R3. 41:

Hardness of a rubber product doesn’t follow the Normal distribution, but the mean and standard deviation of a sample of 36 are 70 and 6 Shore A (the hardness scale). What is the 95% confidence interval for population mean? (Z0.025 = 1.96, Z0.05 = 1.645)

1. A. The distribution is not Normal, so we cannot calculate the confidence interval.
2. B. 68.04 < μ < 71.96
3. C. 68.355 < μ < 71.345
4. D. The population standard deviation is not known so we cannot calculate the confidence interval.

Answer 1

B. 68.04 < μ < 71.96

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± Z*σ/sqrt(n)

From given data, we have

Xbar = 70

σ = 6

n = 36

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence interval = Xbar ± Z*σ/sqrt(n)

Confidence interval = 70 ± 1.96*6/sqrt(36)

Confidence interval = 70 ± 1.9600

Lower limit = 70 - 1.96 = 68.04

Upper limit = 70 + 1.96 = 71.96

Confidence interval = (68.04, 71.96)

B. 68.04 < μ < 71.96