Mathematics, 20.03.2020 10:36 mosthatedpicky1

What sample size would be required to estimate the true proportion of American female business executives who prefer the title "Ms.," with an error of ±0.025 and 98 percent confidence? (Enter your answer as a whole number (no decimals). Use a z-value taken to three decimal places in your calculations.) Sample size

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Answer from: miajustina123

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.326})^2}=2164.1104$

And rounded up we have that n=2165

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 98% of confidence, our significance level would be given by $\alpha=1-0.98=0.02$ and $\alpha/2 =0.01$ . And the critical value would be given by:

$z_{\alpha/2}=-2.326, z_{1-\alpha/2}=2.326$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

(b)

We can assume that the estimated proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.326})^2}=2164.1104$

And rounded up we have that n=2165

Answer from: Quest

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i

Answer from: Quest

Dbc if u do the math and stuff that what i got let me know if i was wrong

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