Question

Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 98% confidence. Assume that s = 14 based on earlier studies.

Answer 1

Answer: 67

Step-by-step explanation:

Formula to calculate sample size: $n=(\dfrac{z^*\times s}{E})^2$ , where s = standard deviation on prior studies , z* = two tailed critical value for confidence level , E = margin of error

Given: E = 4 , s= 14 and confidence level = 98%

Z-value for  98% confidence = 2.326

Then, required sample size: $n=(\dfrac{2.326\times 14}{4})^2=(8.141)^2=66.275881\approx67$

Hence, the required sample size = 67 .