Find the confidence interval Of 57 bank customers depositing a check, 25 received some cash back.(a) Construct a 90 percent confidence interval for the proportion of alldepositors who ask for cash back. (Round your answers to 4 decimalplaces.)The 90% confidence interval is fromto(b) May normality of p be assumed?YesNo

Answered: Of 57 bank customers depositing a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Find the confidence interval

Of 57 bank customers depositing a check, 25 received some cash back.
(a) Construct a 90 percent confidence interval for the proportion of all
depositors who ask for cash back. (Round your answers to 4 decimal
places.)
The 90% confidence interval is from
to
(b) May normality of p be assumed?
Yes
No

Expert Solution

Step 1

Given, Total number of persons, n = 57

number of persons who received cashback is = 25

The proportions of persons who received cashback is, $\hat{p}$ = 25/57 = 0.4386

Since np >10 sampling distribution of sampling proportion is approximately normal. Therefore, a 90% confidence interval for the true proportion of persons who received cashback is given by

$\hat{p} \pm 1.645 \sqrt{\hat{p} (1 - \hat{p}) / n} = 0.4386 \pm 1.645 \sqrt{0.4386 \times 0.5614 / 57} = 0.4386 \pm 0.1081 = 0.3305 t o 0.5467$

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