Question

A College Board sample estimated the standard deviation of 2016 SAT scores to be 194 points. You are researching the average SAT score. You want to know how many people you should survey if you want to know, at a 98% confidence level, that the sample mean SAT score is within 50 points of the true mean SAT score. What value for z should you use in the sample size formula?

a) 1.282
b) 1.645
c) 1.960
d) 2.326

Answer 1

To calculate the sample size needed to estimate the mean SAT score within a certain range at a 98% confidence level, use the formula n = (Z * σ / E)^2, where Z is the critical value that corresponds to the 98% confidence level.

Step-by-step explanation:

In order to calculate the sample size needed to estimate the mean SAT score within a certain range at a 98% confidence level, we can use the formula:

n = (Z * σ / E)^2

where n is the sample size, Z is the z-value corresponding to the confidence level, σ is the estimated standard deviation, and E is the desired margin of error.

In this case, Z is the critical value that corresponds to a 98% confidence level, which is 2.326.

Therefore, the correct answer is d) 2.326.