Mathematics: Suppose a market researcher wants to determine the current percentage of online shoppers who are males. how many online shoppers should the researcher survey in order to be 90% confident that the estimated (sample) proportion is within 3 percentage points of the true population proportion of online shoppers who are males? zo.10 zo.05 zo.01 zo.005 zo,025 1.282 1.645 2.326 2.576 1.960 use the table of values above. do not round until the final step.

Hey there!The domain is the range of possible x values.Thus, the domain here is: [-4, 0]. By the way, I think you made a typo in one of your answer choices.Let me know if this helps :)...

Suppose a market researcher wants to determine

Ответ:

djgunderson

16.06.2020

Mathematics

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.645})^2}=751.674$

And rounded up we have that n=752

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

$\hatt p$ 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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.645, z_{1-\alpha/2}=1.645$

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 $ME =\pm 0.03$ (3 percentage points) and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (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:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.645})^2}=751.674$

And rounded up we have that n=752

0,0(0 оценок)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question