Question

"How much do students pay, on average, for textbooks during the first semester in college? From a random sample of 400 students the mean cost was found to be $357.75 ,and the sample standard deviation was $37.89. Assuming that the population is normally distributed, find the margin of error of a 95% confidence interval for the population mean. Compute the confidence interval and describe in words what it means."

Answer 1

Answer: The margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.

Step-by-step explanation:

Since we have given that

Sample size = 400

Mean = $357.75

Standard deviation = $37.89

At 95% confidence level, z = 1.96

We first find the margin of error.

Margin of error is given by

$z\times \dfrac{\sigma}{\sqrt{n}}\\\\=1.96\times \dfrac{37.89}{\sqrt{400}}\\\\=3.71$

95% confidence interval would be

$\bar{x}\pm \text{margin of error}\\\\=357.75\pm 3.71\\\\=(357.75-3.71,357.75+3.71)\\\\=(354.04,361.46)$

Hence, the margin of error = 3.71, confidence interval = (354.04, 361.46) and it means that mean cost is lies within the confidence interval.