Mathematics: Examine the required sample size needed to be able to estimatethe mean dollars that each consumer will spend each month. desireis to be within plus or minus $10 of the true mean with a 98%confidence level. the standard deviation is thought to be500. what are the trade-offs that will occur when you lower thesample level to 2000?

Examine the required sample size needed to be able

Ответ:

mova1o

14.01.2022

Mathematics

$n=(\frac{2.33(500)}{10})^2 =13572.25 \approx 13573$

And if we use a sample level of n =2000 the margin of error would be higher as we can see here:

$ME=2.33\frac{500}{\sqrt{2000}}=26.05$

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=500$ represent the population standard deviation assumed

n represent the sample size (variable of interest)

Confidence =98% or 0.98

ME = 10 represent the margin of error desired

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =10 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.33$ , replacing into formula (b) we got:

$n=(\frac{2.33(500)}{10})^2 =13572.25 \approx 13573$

So the answer for this case would be n=13573 rounded up to the nearest integer

And if we use a sample level of n =2000 the margin of error would be higher as we can see here:

$ME=2.33\frac{500}{\sqrt{2000}}=26.05$

0,0(0 оценок)

Ответ:

Fsamrai

18.08.2020

Mathematics

Replace x with 0 and solve:

4(0) - 3 = 0-3 = -3

Replace x with 1 and solve:

4(1) - 3 = 4-3 = 1

Rate of change = change in Y over the change in x

Change in Y = 1 - -3 = 1+3 = 4

Change in x = 1-0 = 1

Rate of change = 4/1 = 4

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