Question

A recent survey asked 5,324 individuals: What’s most important to you when choosing where to live? The responses are shown by the following frequency distribution.

Response	Frequency
Good Jobs	1,969
Affordable homes	799
Top Schools	586
Low Crime	1,225
Things to do	745

Calculate the margin of error used in the 95% confidence level for the population proportion of those who believe that low crime is most important.

Calculate the margin of error used in the 95% confidence level for the population proportion of those who believe that good jobs or affordable homes are most important.

Explain why the margins of error in parts a and b are different.

anyones help is really apperciated how to work this problem in EXCEL and what are the FUNCTIONS used. (using discrpitive statistics tool)

thanks a lot

Answer 1

For finding confidence interval for population proportion we used Z critical value ( Z_c ) for given level of confidence.

Here confidence level = c = 0.95

= level of significance = 1- c = 1 - 0.95 = 0.05

So

Now using " =NORMSINV(0.975)" this excel command to get Z_c

So Z_c = 1.96

The formula of margin of error for finding confidence interval of population proportion is as follows.

Where n = total frequency = 5324

= sample proportion.

The number of individuals who believe that low crime is most important are 1225

Therefore, = 1225/5324 = 0.23

so 1 - = 1 - 0.23 = 0.77

The margin of error is as follows.

Also, we can direct use "=CONFIDENCE(0.05,0.00577,1)" this excel command to find the margin of error (E) for population proportion.

Here alpha = 0.05,

Standard deviation =

and use sample size = 1 (because here we use normal approximation to the binomial).

Next we need to find margin of error for good jobs.

Let's find .

= 1969/5324 = 0.3698

So margin of error = E ="=CONFIDENCE(0.05,0.006616,1)" = 0.012967

The margin of error is maximum for the sample proportion is equal to 0.5.

It is small if the sample proportion is far from 0.5

The most closest sample proportion to 0.5 is for second part. So its margin of error is larger of part 2 than part 1.