A researcher takes a very large,nationwide random sample of 7th grade students and computes a mean verbal ability score of 85.50 with a standard deviation of 8.35.From this information,she computes a standard error of the mean of 2.64.What are the upper and lower limits of the 95% confidence interval for the mean?
A)69.13 to 101.87
B)77.15 to 93.85
C)80.33 to 90.67
D)82.86 to 88.14

Question

Quizplus · Accepted Answer

Using the formula for calculating the confidence interval:

Lower Limit = Mean - (z-score * standard error)
Upper Limit = Mean + (z-score * standard error)

where the z-score for a 95% confidence interval is 1.96

Lower Limit = 85.50 - (1.96 * 2.64) = 80.33
Upper Limit = 85.50 + (1.96 * 2.64) = 90.67

Therefore, the 95% confidence interval for the mean is 80.33 to 90.67. Option C is the correct choice.

A Researcher Takes a Very Large,nationwide Random Sample of 7th