You wish to learn the proportion of MBA students that are female within 3%, and with 98% confidence. How large of a sample should you get?
Try this formula:
n = [(z-value)^2 * p * q]/E^2
= [(2.33)^2 * .5 * .5]/.03^2
I'll let you finish the calculation.
Note: n = sample size needed; .5 (if no value is stated in the problem) for p and .5 (which is 1 - p) for q. E = maximum error, which is .03 (3%) in the problem. Z-value is found using a z-table (for 98%, the value is approximately 2.33). Symbols: * means to multiply and ^2 means squared.
I hope this will help get you started.
1504
In order to determine the sample size for estimating the proportion of MBA students that are female within a given margin of error and confidence level, you can use a formula called the sample size formula for proportions. The formula is as follows:
n = (Z^2 * p * (1 - p)) / E^2
Where:
- n is the required sample size
- Z is the Z-score associated with the desired confidence level (in this case, 98% confidence level)
- p is the estimated proportion of success (in this case, the proportion of MBA students that are female)
- E is the desired margin of error (in this case, 3%)
To find the Z-score corresponding to a 98% confidence level, you can use a Z-table or a statistical calculator. The Z-score will be approximately 2.33.
Now, you need to estimate the proportion of MBA students that are female. If you have a prior estimate, you can use that value. Otherwise, you can use 0.5 (50%) as a conservative estimate, as it provides the largest sample size.
Substituting the values into the formula:
n = (2.33^2 * 0.5 * (1 - 0.5)) / 0.03^2
n = (5.4289 * 0.25) / 0.0009
n ≈ 1202.4444
Since you cannot have a fraction of a student, round up the sample size to the nearest whole number. Therefore, to estimate the proportion of MBA students that are female within a 3% margin of error and with 98% confidence, you should get a sample size of at least 1203 MBA students.