Question

1) (15%) For Applied Management Statistics class you want to know how college students feel about the transportation system in Barcelona. a) What is the population in this study? b) What type of sample would you use and why? 2) (25%) A manager of an e-commerce company would like to determine average delivery time of the products. A sample of 25 customers is taken. The average delivery time in the sample was four days. Suppose the delivery times are normally distributed with a standard deviation of 1.2 days. a) Provide a 95% confidence interval for the mean delivery time. b) The manager claims that the average delivery time of their products does not exceed 3 days. Write the null and alternative hypothesis regarding to the claim of the manager. c) Test the manager's claim at 95% confidence level. d) Write the conclusion of your result 3) (15%) For an effective parental skill study, a researcher asked: How many hours do your kids watch the television during a typical week in Barcelona? The mean of 100 Kids (ages 6-11) spend about 28 hours a week in front of the TV. Suppose the study follows a normal distribution with standard deviation 5. a) Estimate the mean of all kids (ages 6-11) in Barcelona, using 99% confidence interval. (show all the calculations) b) Write the conclusion of your result 4) (25%) A regression analysis has been conducted between the annual income (in 1000 euros) and the work experience in years) of people with 0.05 significance level. The results are summarized below. a) Define the independent and dependent variables. What can you say about the correlation between them.

Answer 1

Question 1: a) The population in this study is the college students of Barcelona. b) The clustered sample can be used where first, the colleges of Barcelona can be sampled and then from these sampled colleges, further students can be sampled. Question 2: a) The 95% confidence interval is, C1 = 3tza = 4 2005 2 = 4+(1.96) (using 2-table) V2 = (3.53.4.47) b) The hypotheses are; Ho: u23 Hu<3 c) The 95% confidence interval is (3.53, 4.47) which does not contain the value 3 or the values that are less than 3. So, the null hypothesis is failed to be rejected.

d) Conclusion: There is insufficient to conclude that the mean delivery time is less than 3 days. Question 3: a) The 99% confidence interval is, CI = 3+2 henne (using 2-table) = 28 20.01.2 mm = 28 +(2.58) =(26.71.29.29) b) it can be concluded that one can be 99% confident that the mean hours spent in front of TV by all kids in Barcelona lies in between 26.71 hours and 29.29 hours.