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mariarad [96]
2 years ago
9

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. A 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)
Required:
Construct a 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.
Mathematics
1 answer:
fiasKO [112]2 years ago
8 0

Answer:

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).

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According to the question,

Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.

First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.

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Secondly "change of origin" when every score in a data set by a constant, its mean get  added or subtracted by the same constant and standard deviation remains constant.

Applying change of origin in the above mean and standard deviation  

Mean: 30 - 4 = 26

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

answer = 15\frac{1}{8} -3\frac{1}{2} -2\frac{3}{4}

step 1 find a common denominator

common denominator - 8

* apply *

\frac{1^*^1}{8^*^8} =\frac{1}{8} \\\\\frac{1^*^4}{2^*^4} =\frac{4}{8} \\\\\frac{3^*^2}{4^*^2} =\frac{6}{8}

now we have

15\frac{1}{8} -3\frac{4}{8} -2\frac{6}{8}

step 2 make each fraction a improper fraction

We can do this my multiplying the big number by the denominator and adding that to the numerator.

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now we have

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Now we can subtract

remember when subtracting fractions you only subtract the numerators. ( so we keep the denominator as 8 )

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finally we want to change the answer back into a mixed fraction

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Answer:

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Rectangle;

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We know that

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Hope it helps.

5 0
3 years ago
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