Can someone help me with a Statistic problem?

[nickelanddimed]

Consider a survey of n people asking whether they plan to use Route A or Route B, with an anticipated fraction p choosing Route A.

If p = .30, plot the 95% confidence bounds and the expected value of X as a function of n, for n = 50 to n = 800.

I have no idea where to start or how to work it out..can someone please guide me through the problem.

 

[Astronuc]

There are two possible outcomes - a person chooses A or B, so a binomial distribution applies.

What have you learned about the expectation value?

 

[piercas]

Of course, I am happy to assist you with this statistic problem. It seems like you are trying to analyze the results of a survey regarding the preferred route of a group of people. The first step would be to determine the sample size (n) and the anticipated fraction (p) of people who plan to use Route A. In this case, n represents the total number of people surveyed and p represents the proportion of those people who chose Route A.

To plot the 95% confidence bounds and the expected value of X, we would need to calculate the standard error and margin of error. The standard error is a measure of how much the sample mean varies from the true population mean, and the margin of error is the range within which the true population mean is likely to fall.

To calculate the standard error, we would use the formula SE = √(p(1-p)/n), where p is the anticipated fraction and n is the sample size. Using your given value of p = 0.30 and a sample size of n = 50, the standard error would be SE = √(0.30(1-0.30)/50) = 0.073.

Next, we can calculate the margin of error by multiplying the standard error by the critical value for a 95% confidence interval. The critical value can be found using a table or a calculator, and for a sample size of 50, it is approximately 1.96. Therefore, the margin of error would be ME = 1.96 * 0.073 = 0.143.

Now, we can plot the 95% confidence bounds by adding and subtracting the margin of error from the anticipated fraction. In this case, the lower bound would be 0.30 - 0.143 = 0.157 and the upper bound would be 0.30 + 0.143 = 0.443. This means that we can be 95% confident that the true proportion of people who plan to use Route A falls between 0.157 and 0.443.

To calculate the expected value of X, we would simply multiply the anticipated fraction by the sample size. In this case, the expected value of X would be 0.30 * 50 = 15. This means that we can expect approximately 15 people out of the 50 surveyed to choose Route A.

To plot the expected value of X as a function