Question

A simple random sample of 15 pistons is selected from a large population whose diameters are known to be normally distributed. The sample standard deviation of the piston diameters is s = 2.0 mm. Find a 95% confidence interval for the population variance �

Answer 1

Answer:

95% confidence interval for the population variance is (2.89, 5.11)

Step-by-step explanation:

Confidence Interval (CI) = variance + or - (t×s)/√n

Standard deviation (s) = 2, variance (s^2) = 2^2 = 4, n = 15, degree of freedom = n - 1 = 15 - 1 = 14

t-value corresponding to 14 degrees of freedom and 95% confidence interval is 2.145

Lower bound = variance - (t×s)/√n = 4 - (2.145×2)/√15 = 4 - 1.11 = 2.89

Upper bound = variance + (t×s)/√n = 4 + (2.145×2)/√15 = 4 + 1.11 = 5.11

95% confidence interval is (2.89, 5.11)