Question

The scores on an examination in finance are approximately normally distributed with mean 500 and an unknown standard deviation. The following is a random sample of scores from this examination

401,415.459,462, 524,565

Find a 90% confidence interval for the population standard deviation.

Answer 1

To find the 90% confidence interval for the population standard deviation, first calculate the sample variance. Then, find the critical values for the chi-squared distribution. Finally, calculate the confidence interval using the formula.

Step-by-step explanation:

To find the 90% confidence interval for the population standard deviation, we can use the chi-squared distribution. First, we need to calculate the sample variance, which is the sum of the squared differences between each score and the sample mean divided by the sample size minus one. In this case, the sample variance is 9018.4. Then, we can find the critical values for the chi-squared distribution with n-1 degrees of freedom, where n is the sample size. For a 90% confidence interval, the critical values are 33.924 and 9.348. Finally, we can calculate the confidence interval using the formula: sample variance multiplied by (n-1) divided by the upper and lower critical values:

CI = (n-1) * sample variance / (upper critical value, lower critical value)

CI = (6-1) * 9018.4 / (33.924, 9.348)

CI = 1803.68 / (33.924, 9.348)

CI = (53.13, 1830.32)