5. Suppose a larger (independent) random sample of 100 Ann Arbor residents is taken and the 90%confidence interval was calculated to be (0.54, 0.70). How many of the 100 Ann Arbor residents in thissample plan on reading a book next month? Additionally, what is the 90% margin of error for this90% confidence interval? Hint: don't overthink this one!

Name: 5. Suppose a larger (independent) random sample of 100 Ann Arbor resi
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Description: 5. Suppose a larger (independent) random sample of 100 Ann Arbor residents is taken and the 90%confidence interval was calculated to be (0.54, 0.70). How many of the 100 Ann Arbor residents in thissample plan on reading a book next month? Additional

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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5. Suppose a larger (independent) random sample of 100 Ann Arbor residents is taken and the 90%
confidence interval was calculated to be (0.54, 0.70). How many of the 100 Ann Arbor residents in this
sample plan on reading a book next month? Additionally, what is the 90% margin of error for this
90% confidence interval? Hint: don't overthink this one!

Expert Solution

Step 1: Introduction

The number of random samples is $n = 100$

The 90% confidence interval is $(0.54, 0.70)$ so the

lower limit $= 0.54$

Upper limit $= 0.70$

$α = 0.1$

Now, the confidence interval for the mean is given as

$x - Z_{\frac{α}{2}} (\frac{s}{\sqrt{n}}) < μ < x + Z_{\frac{α}{2}} (\frac{s}{\sqrt{n}})$ $(f o r n > 30)$

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