Assume that all grade-point averages are to be standardized on a scale between 0 and 5 . How many grade-point averages must be obtained so that the s Assume that a \( 98 \% \) confidence level is desired. If using the range rule of thumb, \( \sigma \) can be estimated as \( \frac{\text { range }}{4}=\frac{5-0}{4}=1.25 \). Does the sample size seem The required sample size is (Round up to the nearest whole number as needed.)
Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
Bonus Knowledge
To determine the required sample size for a \( 98 \% \) confidence level, you can use the formula: \[ n = \left( \frac{Z \cdot \sigma}{E} \right)^2 \] Here, \( Z \) is the Z-score corresponding to the \( 98 \% \) confidence level (which is approximately \( 2.33 \)), \( \sigma \) is the estimated standard deviation (\( 1.25 \)), and \( E \) is the margin of error you are willing to accept. Let's say you want a margin of error of \( 0.5 \). Plugging these values into the formula gives: \[ n = \left( \frac{2.33 \cdot 1.25}{0.5} \right)^2 \approx \left( 5.8125 \right)^2 \approx 33.8 \] Rounding up gives you a required sample size of \( 34 \). This ensures you have a robust sample to make confident inferences about the average grade-point average within the specified range, while capturing enough variability with the standard deviation you've estimated.