Question

A GLo tutoring company would hike to estimate the current percentage of non-high school graduates. (a) How many people should be surveyed in order to estimate the proportion of han-high school graduatei within 4% with 95% contidence? (b) Suppose the tutoring company wanted to cut the margin of error to 3%. How many people should be sampled now? (c) In a certain rural ares, the percent of people without a GED was thought to be 71%. How many people sheuld be sampled in thia reglon to eatimate the propertion without a Ge0 whin 5% ?

Answer 1

To calculate the sample size needed to estimate the percentage of non-high school graduates, apply the sample size formula for proportions using the Z-score for the desired confidence level, an estimated population proportion, and the specified margin of error.

Step-by-step explanation:

To estimate the current percentage of non-high school graduates with a specified margin of error and confidence level, one can use the sample size formula for proportions. This formula is:

n = (Z^2 * p * (1-p)) / E^2

Where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion of the population, and E is the margin of error.

1. (a) Assuming no initial estimate available for p, one often uses 0.5 for maximum variability. For a 95% confidence level, the Z-score would be approximately 1.96. With a margin of error of 4%, the calculation would be: n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2.
2. (b) Using the same formula but changing the margin of error to 3%, the new sample size should be calculated accordingly.
3. (c) Assuming a 71% rate of non-GED individuals in a rural area, with a desired margin of error of 5% and the same 95% confidence level, the specific sample size for this proportion should be computed using p = 0.71.