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**(Round all intermediate calculations to at least 4 decimal places.)**

A random sample of 25 observations is used to estimate the population variance. The sample mean and sample standard deviation are calculated as 52.5 and 3.8, respectively. Assume that the population is normally distributed. Use Table 3.

**a.**Construct the 90% interval estimate for the population variance. **(Round your answers to 2 decimal places.)**

Confidence interval to

**b.**Construct the 99% interval estimate for the population variance. **(Round your answers to 2 decimal places.)**

Confidence interval to

**c.**Use your answers to discuss the impact of the confidence level on the width of the interval. The width of the interval increases with the confidence level.The width of the interval decreases with the confidence level.

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