A psychologist has designed a new intelligence test.Historically,time to complete the old test was normally distributed with a standard deviation of 5 minutes.A sample of 50 new test taking times yielded an average time of 118 minutes.The 99% confidence interval for the average test taking time is _____.
A)[116.18,119.82]
B)[116.36,119.64]
C)[116.61,119.39]
D)[115.67,120.33]
E)[115.82,120.18]

Question

Quizplus · Accepted Answer

To calculate the 99% confidence interval for the average test-taking time, we use the formula for the confidence interval for the mean, which is $\bar{x} \pm z\frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-score corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and $n$ is the sample size. Given that the sample mean $\bar{x} = 118$ minutes, the standard deviation $\sigma = 5$ minutes, the sample size $n = 50$, and knowing that the z-score for a 99% confidence level is approximately 2.576, we can calculate the margin of error as $2.576 \times \frac{5}{\sqrt{50}}$, which equals approximately 1.82. Therefore, the 99% confidence interval is $118 \pm 1.82$, which gives us [116.18, 119.82].

A Psychologist Has Designed a New Intelligence Test