Applied Statistics Assignment
Exercise 1 -
The store Sports Town sells athletic equipment and sporting goods. The regional manager of Sports Town believes that the stores in her region are not selling enough running shoes and would like to increase this number. The regional manager examines how many pairs of running shoes are sold per week in each of the 37 stores. Then an advertising campaign is carried out on the radio for Sports Town running shoes. After the campaign, the manager records how many pairs of running shoes are sold per week to see whether the advertising campaign has been effective in increasing sales. Use the SPSS dataset Sales to answer the following questions:
1. What is the appropriate null hypothesis?
2. What is the appropriate alternative hypothesis?
3. Report the mean and standard deviation for sales before the advertising campaign.
4. Report the mean and standard deviation for sales after the advertising campaign.
5. What is the 95% confidence interval of the mean difference?
6. If we assume that α = 0.05, should we reject the null hypothesis? Why or why not?
7. Interpret the results from this test. Has the advertising campaign been effective?
Exercise 2 -
An instructor has a class of 23 students. At the beginning of the semester, each student is randomly assigned to one of four teaching assistants - Jessica, John, Kate and Sam. The students are encouraged to meet with their assigned teaching assistant to discuss difficult course material. At the end of the semester, a common examination is administered. The scores obtained by students working with these teaching assistants are shown in the dataset Teaching. Use the dataset and perform a Kruskal-Wallis test of the null hypothesis that the population mean test scores are the same for students assigned to the four teaching assistants.
1. Report the results from Kruskal-Wallis, rejection rule, conclusion of the test and its interpretation, given a 5% significance level.
2. In the SPSS output, what does the value for Mean Rank refer to?
3. When do we use Kruskal-Wallis test?
4. Present a histogram for each of the teaching groups against a normal curve. Interpret what this information tells us.
Exercise 3 -
You are interested in comparing grades of Business students at Reykjavik University (RU) to Business students at the University of Iceland (UI). You believe that the grades between the two schools are different. The SPSS dataset Grades contains average grades of 55 Business students at RU and average grades of 55 Business students at UI. The grades can take a value from 0 to 10. Assume that α = 0.05.
1. What is the appropriate null hypothesis?
2. What is the appropriate alternative hypothesis?
3. Conduct the correct statistical test. Report the results and interpret them.
4. Are the variances in the groups equal? How can you tell?
5. What are the assumptions we make when we conduct this particular statistical test?
Exercise 4 -
A marketing company is interested in seeing which type of social media marketing is most successful. The marketing company examines the profits of 30 brands that focus their social media efforts on Facebook, 30 brands that focus their social media efforts on Instagram and 30 brands that focus their social media efforts on Snapchat. Profits are recorded in millions of US dollars. Use the SPSS dataset Social media to answer the following questions:
1. What is the appropriate null hypothesis?
2. What is the appropriate alternative hypothesis?
3. What is the mean and standard deviation of profits for brands that focus on Facebook?
4. What is the mean and standard deviation of profits for brands that focus on Instagram?
5. What is the mean and standard deviation of profits for brands that focus on Snapchat?
6. Conduct the appropriate statistical test to see whether the means for the three groups are different. Report and interpret this information, assuming that α = 0.05.
7. Which means are different from each other?
8. Using this information, what social media strategies would you recommend?
Exercise 5 -
An anthropologist was interested in the effects of alcohol on mate selection in night clubs. The anthropologist is testing the "Beer goggles effect," which is that after consuming alcohol, people are no longer able to tell whether other people are attractive. The anthropologist also thinks that this might work differently for men and women. The anthropologist took 48 students to a bar (24 male and 24 female) and gave one group only alcohol-free drinks, one group got two strong alcoholic drinks and the last group got four strong alcoholic drinks. At the end of the evening the anthropologist took a picture of the person each participant was chatting up and got a group of judges to rate that person´s attractiveness (on a scale of 0 to 100). Conduct the appropriate statistical test to examine whether alcohol consumption influences attractiveness, whether gender influences attractiveness and whether the effects of alcohol on attractiveness differ by gender. Assume that α = 0.05. Use the SPSS dataset Beer goggles to answer the following questions:
1. What are the appropriate null hypotheses?
2. What are the appropriate alternative hypotheses?
3. What is the value of the sum of squares for gender and what does this number represent?
4. What is the F value for alcohol consumption?
5. Is alcohol consumption connected with attractiveness? Provide evidence for your answer.
6. If attractiveness differs by alcohol consumption, are all the groups different from each other? How can you find this information? Explain your answer.
7. Is gender of participants connected with attractiveness? Provide evidence for your answer.
8. Does alcohol have different effects on attractiveness for men and women? Provide evidence for your answer.
9. Draw a plot of the combined effect of alcohol consumption and gender on attractiveness and describe the results.
Attachment:- Assignment Files.rar