Question

A Math Professor records his commuting time to work on 23 days, finds a sample mean of 12 mins 45 seconds and standard deviation of 55 seconds. Suppose a normal quintile plot suggests the population is approximately normally distributed. If we are interested in creating a 95% confidence interval for σ, the population standard deviation, then: a) What are the appropriate χ2R and χ2L values, the Right and Left Chi-square values? Round your responses to at least 3 decimal places. χ2R= Number χ2L= Number b) Next we construct the appropriate confidence interval. Complete the statements below (rounding each of your interval bounds to at least 3 decimal places): Context: "We are Number % confident that the true standard deviation of the professor's Preview time to work lies between Number and Number Units "

Answer 1

Solution :

Given that,

s = 55

s² = 3025

n = 23

Degrees of freedom = df = n - 1 = 23 - 1 = 22

At 95% confidence level the ² value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

²_L = ²_/2,df = 36.781

²_R = ²_{1 - /2,df} = 10.982

The 95% confidence interval for is,

(n - 1)s² / ²_/2 < < (n - 1)s² / ²_{1 - /2}

22 * 3025 / 36.781 < < 22 * 3025 / 10.982

42.537 < < 77.844

We are 95% confident that the true standard deviation of the professor's Preview time to work lies between 42.537 and 77.844