Which of the following lines has a zero slope?

The 95% confidence interval for the mean amount of the increase is ($541.6, $588.4). This means that we are 95% sure that the mean amount of increase of all customers who charge at least $3,000 in a year is between these two values.

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:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{267}{\sqrt{500}} = 23.4$

The lower end of the interval is the sample mean subtracted by M. So it is 565 - 23.4 = $541.6

The upper end of the interval is the sample mean added to M. So it is 565 + 23.4 = $588.4

The 95% confidence interval for the mean amount of the increase is ($541.6, $588.4). This means that we are 95% sure that the mean amount of increase of all customers who charge at least $3,000 in a year is between these two values.

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3 years ago