Lesson 8: Hypothesis Testing LAB 1 | Complete Solution

Answer the following questions showing all work.  If you use Minitab Express include the appropriate output (copy + paste) along with an explanation.  Round all answers to 3 decimal places. If you have any questions, post them to the course discussion board. 
(14 points)

1. A company is trying to determine whether or not to advertise on Twitter based on the average time a user spends on Twitter per month.  If the average time is over 180 minutes they plan to purchase $1 million extra on Twitter advertising.    
A. Write out the null and alternative hypotheses of this test using the appropriate symbols.  For a review of using the equation editor in Word, see https://onlinecourses.science.psu.edu/statprogram/equations 
B. In terms of this scenario, describe what a Type I error would look like. (Be sure to apply this scenario!)  
C. In terms of this scenario, describe what a Type II error would look like. (Be sure to apply this scenario!)  
D. The researchers took a sample of 1000 users and found a sample mean time of 185 minutes with a standard deviation of 20 minutes.  Calculate the test statistic (either by hand or use Minitab Express https://onlinecourses.science.psu.edu/stat200/node/228)
E. What is the p-value associated with the test statistic you computed in part D?
F. Are the results of this study statistically significant? Explain why.
G. If you were this company, would this be enough evidence for you to spend $1 million on advertising with Twitter? Explain why or why not.

2. Answer the following questions using the dataset Summer17Data.MTW Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students.  

A.  Use Minitab to perform the hypothesis test that the mean height of all Penn State World Campus STAT 200 students is under 70 inches. 
B.  Based on the results from part A, do you have evidence to believe that the mean height of all Penn State World Campus Stat 200 students is under 70 inches at .05 alpha level?
C. In part A, is it possible that a Type I or Type II error was committed?  Explain Why.
D. Using Minitab construct a 95% confidence interval for the proportion of the population that is dieting to lose weight. Use the normal approximation method if appropriate.

E. Using Minitab, test that the proportion of this population that is dieting to lose weight is different from 50%? Assume that in the population this variable is normally distributed.  Use the normal approximation method if appropriate.

F.  Based on your answers from part E, is there evidence that 50% of the population of World Campus Stat 200 students is dieting to lose weight?

G. Compare your results from part D and part E. Explain how these two results could be used to answer the same research question.