Question

Stock Prices A random sample of stock prices per share (in dollars) is shown. Find the 95% confidence intervals for the variance and standard deviation for the prices. Assume the variable is normally distributed. Use a graphing calculator and round the answers to two decimal places. 14.75 46.12 10.87 40.25 60.50 28.00 28.25 6.94 45.12 13.62 53.81 3.81 43,00 47.50 7.50 75.37 12.00 28.37 Serdote State 247.549<o? < 948.13 15.3 <o< 30.79

Answer 1

Solution:-

=> 95% Confidence interval for the variance = 248.81 < σ^2 <993.09

=> 95% Confidence interval for the standard deviation = 15.77 < σ < 31.51.

Explanation:

Therefore, the sample variance is computed as shown below: - m - (2x)) = 1B- (25295.0572 - 565.75") = 441.8785 Therefore, based on the data provided, the sample variance is s? = 441.8785. The critical values for a = 0.05 and df = 17 degrees of freedom are xź = xi-a/2.1-1 = 7.5642 and x = x2.-1 = 30.191. The corresponding confidence interval is computed as shown below: CI(Variance) = (n-1) s (n-1)s ( x 2,1-1 -a 2,n-1) (18 - 1) 441.8785 (18-1) 441.8785 30.191 7.5642 = (248.8136,993.0922) Now that we have the limits for the confidence interval, the limits for the 95% confidence interval for the population standard deviation are obtained by simply taking the squared root of the limits of the confidence interval for the variance, so then: CI(Standard Deviation) = (248.8136, 1993.0922) = (15.7738, 31.5134) Therefore, based on the data provided, the 95% confidence interval for the population variance is 248.813602 <993.0922, and the 95% confidence interval for the population standard deviation is 15.7738 < <31.5134.