A random sample of 14 college female students revealed their average height was 66.1 inches.

a) How many students should be in a samle if a 95% confidence interval is to have a margin of error of only plus/minus 1 inch?

Is that the only information you were given? Were you not told the standard deviation for the 14 that were measured? It seems to me that you need some infomation on the inherent variability of the height distribution. None has been provided.

Here is the complete problem:
A random sample of 14 college female students revealed their average height was 66.1 inches.
a) Explain to someone who knows no statistics why we can't just say that 66.1 inches is the average height of all female students.
b) Te researcher announced a margin or error of plus/minus 1.75 inches for 95% confidence. Write down the 95% confidence interval for the height of all female students. Explain clearly what"95% confidence" means.
c) State the formula for the margin of error of a confidence interval for the mean. Explain what each term in this expression represents. Explain how changing these terms one at a time will affect the size of the confidence interval.
d) How many students should be in a sample if a 95% confidence interval is to have a margin of error of only plus/minus 1 inch?

Can you help me further? Thanks.

The standard error of the mean (SE) = the standard deviation (SD) divided by the square root of n - 1.

SE = SD/sq rt (n-1)

You have the values of SE and n. Substitute those into the formula to get the SD. Then use this SD and SE of 1 to find your new n value.

This should answer your original question. Thanks for asking.

Thank you for the clarification...very appreciated. K

a) We can't just say that 66.1 inches is the average height of all female students because the 66.1 inches is based on a random sample of only 14 college female students. This sample may not accurately represent the entire population of college female students. To make a general statement about the average height of all female students, we need a larger and more representative sample.

b) A 95% confidence interval is a range of values within which we are 95% confident that the true population parameter (in this case, average height) falls. It takes into account the margin of error to reflect the uncertainty in the estimation.

To calculate the confidence interval, we start with the sample mean (66.1 inches) and add/subtract the margin of error (1.75 inches) to create the range of values. So the 95% confidence interval for the height of all female students would be [66.1 - 1.75, 66.1 + 1.75] or [64.35, 67.85] inches.

c) The formula for the margin of error of a confidence interval for the mean is:

Margin of error = critical value * standard error

The critical value depends on the desired confidence level and is determined using statistical tables or software. The standard error (SE) represents the variability of sample means around the population mean and is calculated using the sample standard deviation (SD) and the sample size (n).

As for the effect of changing each term on the size of the confidence interval:
- Increasing the confidence level will result in a wider interval as it requires capturing a higher percentage of the population.
- Increasing the standard deviation (SD) will result in a wider interval as it reflects more variability in the population.
- Increasing the sample size (n) will result in a smaller interval as it provides more precision in estimating the population mean.

d) To determine the required sample size for a 95% confidence interval with a margin of error of plus/minus 1 inch, we need to use the formula mentioned earlier:

Margin of error = critical value * standard error

Rearranging the formula to solve for the sample size (n):

n = [(critical value * SD) / margin of error]^2

Given that the margin of error is 1 inch, we can substitute this value along with the critical value and the standard deviation (which we can calculate from the given information) into the formula to determine the required sample size.