Question

# A questionnaire about study habits was given to a random sample of students taking a large...

A questionnaire about study habits was given to a random sample of students taking a large introductory stats class. The sample of 35 students reported that they spent an average of 115 minutes per week studying stats. Assume that the standard deviation is 40 minutes.

A) Give a 95% confidence interval for the mean time spent studying stats by students in this class.

B) Is it true that 95% of the students in the class have weekly studying times that lie in the interval you found in (A)? Explain

Sample size = n = 35

Sample mean = = 115

Population standard deviation = = 40

A) We have to construct 95% confidenc interval for the population mean.

Here population standard deviation is known so we have to use one sample z-confidence interval.

z confidence interval

Here E is a margin of error

Zc = 1.96 ( Using z table)

So confidence interval is ( 115 - 13.2520 , 115 + 13.2025) = > ( 101.7480 , 128.2520)

B)

Interpretation: We are 95% confidence that the population mean of the students in the class have weekly studying times that lie in the interval.

So given statement if FALSE.