Question

A random sample of 36 drivers used on average 756 gallons of gasoline per year. The standard deviation of the population is 35 gallons.

(a) Find the 95% confidence interval for the population mean.

Answer 1

To find the 95% confidence interval for the population mean, use the formula: Confidence Interval = Sample mean ± (Critical value) x (Standard deviation / sqrt(sample size)). Calculate the lower and upper bounds of the confidence interval using the given values.

Step-by-step explanation:

To find the 95% confidence interval for the population mean, we can use the formula:

Confidence Interval = Sample mean ± (Critical value) x (Standard deviation / sqrt(sample size))

First, we find the critical value for a 95% confidence level, which corresponds to a Z-value of approximately 1.96. Given that the sample size is 36, the standard deviation is 35 gallons, and the sample mean is 756 gallons, we can plug these values into the formula:

Confidence Interval = 756 ± (1.96) x (35 / sqrt(36))

Simplifying the equation gives us:

Confidence Interval = 756 ± (1.96) x (35 / 6)

Calculating this will give you the lower and upper bounds of the confidence interval.