Question

Bob Nale is the owner of Nale's Gas Station. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. He assumes a population standard deviation of 2.30 gallons. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60. What is the z-statistic for a 99% confidence interval for the population mean.

Answer 1

The z-statistic for a 99% confidence interval for the population mean is -8.47.

Step-by-step explanation:

To find the z-statistic for a 99% confidence interval for the population mean, we first need to calculate the margin of error. The margin of error is the product of the critical value and the standard deviation divided by the square root of the sample size. The critical value for a 99% confidence interval is 2.33 as per the z-table. So the margin of error is (2.33 * 2.3) / sqrt(60) = 0.547. The z-statistic is equal to the ratio of the difference between the sample mean and the population mean to the margin of error. So, the z-statistic is (8.60 - 13) / 0.547 = -8.47.

Answer 2

The z-statistic for a 99% confidence interval for the population mean is 2.575.

Step-by-step explanation:

We have that to find our
`\alpha` level, that is the subtraction of 1 by the confidence interval divided by 2. So:

`\alpha = (1 - 0.99)/(2) = 0.005`

Now, we have to find z in the Ztable as such z has a pvalue of
`1 - \alpha`.

That is z with a pvalue of
`1 - 0.005 = 0.995`, so Z = 2.575.

The z-statistic for a 99% confidence interval for the population mean is 2.575.