Provide an appropriate response.
-Assume that the heights of female executives are normally distributed. A random sample of 20 female executives have a mean height of $62.5$ inches and a standard deviation of $3.7$ inches. Construct a $98 \%$ confidence interval for the population variance, $\sigma ^ { 2 }$.
A) $( 7.2,34.1 )$
B) $( 2.7,5.8 )$
C) $( 1.9,9.2 )$
D) $( 7.6,35.9 )$

Question

Quizplus · Accepted Answer

To construct a 98% confidence interval for the population variance when the sample size is 20 and the sample standard deviation is 3.7, we use the chi-square distribution. The formula involves the sample variance ($s^2$) and the chi-square values for the desired confidence level. The sample variance $s^2$ is $3.7^2 = 13.69$. The degrees of freedom ($df$) is $n - 1 = 19$. For a 98% confidence interval, we look up the chi-square values for $df = 19$ at the lower and upper tails (1% each since it's two-tailed for 98% confidence). The correct interval calculation will match one of the provided options, which is option A, given it's the only one that fits the context of variance values.

Provide an Appropriate Response 62.562.562.5 Inches and a Standard Deviation Of 3.73.73.7

Provide an Appropriate Response $62.5$ Inches and a Standard Deviation Of $3.7$