# Confidence Interval and Hypothesis Testing in Statistics

1. A sample of 25 MBA students taking OTM course in the Spring of 2013 shows an average income of $85,000 with the sample standard deviation of $5,000. Find the 95% confidence interval of the population mean income of MBA students.

2. According to a study, the mean (μ) price of a gallon of the regular gasoline in the United States is $4.15. A sample of 25 Chicago area gas stations shows the mean price of $4.95. The standard deviation (s) of the population is known to be $1.00. Develop a hypothesis test that can be used to determine whether the mean (μ) price of a gallon of the regular gasoline in the Chicago area is different than $4.15 (using the alpha (a) of 5%).

© BrainMass Inc. brainmass.com June 4, 2020, 3:54 am ad1c9bdddfhttps://brainmass.com/statistics/confidence-interval/confidence-interval-hypothesis-testing-statistics-542513

#### Solution Preview

1. First, we use t distrubtion to answer the question because sample size=25<30. so critical value = t(24,0.025)=2.3910.

so 95% confidence interval of the ...

#### Solution Summary

The solution gives detailed steps on calculating the confidence interval for population mean in a specific example. Next, a hypothesis testing for the population mean is performed and explained step by step in another example.