The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

A store randomly samples 603 shoppers over the course of a year and finds that 142 of them made their visit because of a coupon they'd received in the mail.

This means that $n = 603, \pi = \frac{142}{603} = 0.2355$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 - 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2016$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 + 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2694$

The 95% confidence interval for the fraction of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694).

8 0

3 years ago

A rectangle has an area of 226.1 square miles and a base of 13.3 miles. What is the height?

miskamm [114]

Answer:

The width (in our case it is the height) of the rectangle equals 17 miles

Step-by-step explanation:

In order to solve this, we need to know the following...

Area of a rectangle = Length x Width

(in our case based on what you said length is the base and width is the height)

Now we just change the formula to our needs and get that...

Width = Area of the rectangle / Length

And so we get...

Width = Area of the rectangle / Length

Width = 226.1 / 13.3

Width = 17 miles

3 0

3 years ago

A taxi fare has a fixed charge of 1.75 and an additional charge 0.45 per mile. A fare for m miles is 13.90. Which equation could

Pavel [41]

Answer:

The answer is 27 miles and option b will give that.

Step-by-step explanation:

1.75 + 0.45m = 13.90

m = (13.90 - 1.75) / 0.45

m = 27 miles

Hope this helped

3 0

4 years ago