SCMA1000-06W16 ASSIGNMENT 2 (10%) (Due: March 28th, 2016) Topic: Confidence Interval for the population mean 1. (Modified from question #9 page 342 textbook). Please use the data set: Data for Question 1 provided in the Excel file to do this question. This data set provides the time in hours required for 35 individuals to complete their income tax returns. (8 marks) a) Determine the sample mean and sample standard deviation (you can use Excel to do this part). [2] b) Let be the mean time required to complete an income tax return. What is the point estimate of ? [1] c) Construct a 95% confidence interval for the mean time, , using the formula provided in chapter 8 when the population standard deviation is unknown. Run Excel to check your results. [3] d) If we also constructed a 99% confidence interval for the mean time, would the 99% confidence interval be wider or narrower than the 95% confidence interval? Explain. [2] Topic: Confidence Interval for the population proportion 2. A new brand of chocolate bar is being market tested. Four hundred of the new chocolate bars were given to consumers to try. The consumers were asked whether they liked or disliked the chocolate bar. You are given their responses below. (6 marks) Response Liked Disliked Frequency 300 100 400 a) What is the point estimate for the proportion of people who liked the chocolate bar? [1] b) Construct a 95% confidence interval for the true proportion of people who liked the chocolate bar. [3] c) If a new survey is going to be conducted, with 95% confidence level, how large of a sample needs to be taken to provide a margin of error of 4% or less? (use the sample proportion as the planning value, p*) [2] Topic: Hypothesis Testing 3. [Modified from #51 page 411 in the textbook] A recent issue of the AARP Bulletin reported that the average weekly pay for a woman with a high school degree is $600. Suppose you would like to determine if the average weekly pay for all working women is significantly greater than that for women with a high school degree. A sample of 64 working women was selected. The sample mean is $640 and the sample standard deviation is $147. (6 marks) 1 SCMA1000-06W16 a) State the hypotheses that should be used to test whether the mean weekly pay for all women is significantly greater than the mean weekly pay for women with a high school degree. [1] b) At 5% significance level, conduct a hypothesis test using the critical value approach.[3] c) Repeat the hypothesis test using the p-value approach. [2] Topic: Comparing two population means 4. (Modified from Case Problem 3 page 473) Please use the data set: Data for Question 4 provided in the Excel file to do this question. This sample data set provides the annual salary for salespersons employed in inside a local and outside the local sales position. (6 marks) a) Use Excel (t-Test: Two-Sample Assuming Unequal Variances) to conduct a hypothesis to determine whether there is a significant difference in the mean salary between the inside salespersons group and the outside salespersons group. Given = 5%. [3] (Please read the Excel Instruction part II pages 19-20 or textbook page 476) b) Now you are going to use the information you obtained in part a) to construct a confidence interval for the mean salary difference between the two groups using the formula we learned in class. Use the results obtained in the Excel outputs in part a) to fill in the table below. [3] Inside Outside Sample size Sample Mean Sample Standard Deviation Use the information in this table and the formula we learned in chapter 9 to construct a 95% confidence interval for the difference between the population mean salaries of the two groups (use the number of degrees of freedom for the t distribution as the one obtained in the Excel output from part a)). Is the result in part b) consistent with the results in part a)? Instruction: You can work in a group of two on this assignment or work on your own if you prefer. If you work in a group of two, you both should work together on every question to understand how to do each step. The Excel file that contains data sets for this assignment is posted on the course website. (Please click on the Assignment 2 tab.) For questions using Excel, please submit your excel file or copy and paste all the Excel outputs to a Word document to report; For questions doing by hand, clearly show your work to get the full mark for each question. For all decimal results, please keep three decimal places. For money values, please keep two decimal places. 2 SCMA1000-06W16 You can submit your assignment at the beginning of the class on the due date or submit it online via the Dropbox tool on the course website by 11:40 AM on the due date. 3 Data for Question 1 Tax Return Time (hours) 26.5 13.0 49.9 28.8 44.0 61.6 0.5 40.5 34.9 47.9 36.6 24.1 39.8 47.8 18.5 36.6 39.2 14.5 37.3 40.5 49.3 45.5 28.3 19.5 5.6 52.6 41.4 45.3 39.0 33.7 29.4 14.5 40.1 33.7 37.4 This data set provides the time in hours required for 35 individuals to complete their income tax returns. sample mean std deviation 34.2 13.77481 Data for Question 4 Salary for Inside Sales Positions ($) 53938 52694 52031 57718 48621 54768 52282 55632 51827 51948 56588 59253 53464 60949 52833 64562 52644 55959 56339 63799 59057 59457 54122 58814 Salary for Outside Sales Positions($) 72835 63856 68858 63478 83846 83176 72914 83040 64288 88730 77683 71345 78074 65546 66024 79383 61128 78710 75869 76762 60993 61299 82794 77403 78936 78850 74389 86692 77356 This data set contains the Group 1: Salespersons wh Group 2: Salespersons wh the annual salary (in dollars) for two groups of salespersons; s who were employed in Inside sales positions s who were employed in Outside sales positions