A $99 \%$ confidence interval (in inches) for the mean height of a population is $65.33

Question

A $99 \%$ confidence interval (in inches) for the mean height of a population is $65.33 < \mu < 66.87$. This result is based on a sample of size 144 . If the confidence interval $65.54 < \mu < 66.66$ is obtained from the same sample data, what is the degree of confidence? (Hint: you will first need to find the sample mean and sample standard deviation).
A) 93%
B) 92%
C) 95%
D) 94%

Quizplus · Accepted Answer

The width of the confidence interval is related to the degree of confidence. A narrower interval (65.54 to 66.66) compared to the original (65.33 to 66.87) indicates a lower degree of confidence. Calculating the z-scores for both intervals and comparing them shows that the second interval corresponds to approximately 94% confidence.

A 99%99 \%99% Confidence Interval (In Inches) for the Mean Height of a Height

A $99 \%$ Confidence Interval (In Inches) for the Mean Height of a Height