COMM121 (Statistics For Business) UNIVERSITY OF WOLLONGONG FACULTY OF BUSINESS Tutorial 6 Week 9 Questions Please follow this instruction to prepare your homework: Do not print and hand in the questions along with the solutions. Show your full name and student number at the top of the first page. Your homework should be presented neatly and legibly. Homework should be prepared without ragged edges. In the case of problems you must include enough additional information (explanations, formulas and calculations, etc.) to justify your answer. Chapter 10 10.17* Do male law graduates earn more than females? To address this proposition the Law Association collected a sample of salaries (in dollars) from newly graduated males and females. The data were collected and analysed using Excel and this is the output: t-Test: Two-Sample Assuming Equal Variances Mean Variance Observations Pooled Variance Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Female 49925.94444 489142253.2 18 591009716 0 38 -3.565965675 0.00049959 1.68595446 0.000999181 2.024394164 male 77478.18182 673473852.5 22 a. Assuming that the population variances for males and females are equal, is there evidence of male graduates earning higher salaries? (Use = 0.05.) What statistical conclusion can be reached? What action needs to be taken? b. Find the p-value in (a) and interpret its meaning. c. What other assumption is necessary in (a)? 10.18* Repeat problem 10.17(a) assuming that the population variances are not equal. Considering the following output compare the results with those of problem 10.17(a). Excel output: t-Test: Two-Sample Assuming Unequal Variances female Mean 49925.94444 Variance 489142253.2 Observations 18 Hypothesized Mean Difference 0 df 38 t Stat -3.624446816 P(T<=t) one-tail 0.000422668 t Critical one-tail 1.68595446 P(T<=t) two-tail 0.000845335 t Critical two-tail 2.024394164 male 77478.18182 673473852.5 22 10.23* In industrial settings, alternative methods often exist for measuring variables of interest. The data represent measurements in-line (collected from an analyser during the production process) and from an analytical lab. The data were collected and analysed using Excel and this is the output: t Test: Paired Two-Sample for Means In-Line Analytical lab Mean 6.490833 6.49375 Variance 1.179912 1.247928804 Observations 24 24 Pearson Correlation 0.994239 Hypothesized Mean Difference 0 df 23 t Stat -0.11692 P(T<=t) one-tail 0.453968 t Critical one-tail 1.71387 P(T<=t) two-tail 0.907937 t Critical two-tail 2.068655 a. At the 0.05 level of significance, is there evidence of a difference in the mean measurements in-line and from an analytical lab? What statistical conclusion can be reached? What action needs to be taken? b. What assumption is necessary to perform this test? 2 10.58* A motorist wishes to compare the price of petrol in Adelaide and rural South Australia. She collected the following data: Use a level of significance of 0.01. a. Assuming equal variances, is there evidence that the mean petrol price is greater in rural South Australia? What statistical conclusion can be reached? What action needs to be taken? 1) A consumer organisation is concerned about the increase in the level of credit card debt of young consumers. It commissions two surveys, in October 2004 and October 2008 of 1000 consumers aged 18-24 years old. These show an average credit card debt of $5,800 in October 2004 with a standard deviation of $960 compared with an average of $6,320 in October 2008 with a standard deviation of $941. Assuming that the population variances from both years are equal, is there evidence that the mean credit card debt is higher in October 2008 than in October 2004? (use the =0.05 level of significance). What statistical conclusion can be made? 2) The Commercial Bank of Singapore advertises that 'our customers come first' and claims that the waiting time for customer inquiries is the lowest. A sample of 34 of its customers waited an average of 8 minutes with a standard deviation of 2.5 compared to an average of 9.5 minutes with a standard deviation of 5 from a sample of 45 customers at competitors' branches. Assuming that the population variances from both banks are equal, is there evidence that the mean waiting time at the Commercial Bank of Singapore is lower? (Use 0.05 level of significance), What statistical conclusion can be made? 3) Repeat the problem in question 2 assuming that the population variances are not equal. Compare the results with those of problem 2 (assuming that the degree of freedom is 68). 4) The Priority Time Management course is designed to save managers from wasting time on tasks such as checking emails. The following data shows the amount of time in minutes spent checking emails for a sample of six managers both before and after attending the course. At the 0.01 level of significance is there any evidence that the course has reduced the amount of time managers spend checking emails? What statistical conclusion can be made? Manager 1 2 3 Before 23 45 67 After 18 23 50 3 4 5 6 34 12 60 21 13 45 5) Are fruit and vegetables cheaper at a specialist fruit shop or in a supermarket? The following data compare prices for items of similar quality observed at a fruit shop and a supermarket both located in the same shopping complex in Sydney. At 0.01 level of significance is there evidence that the mean price at the specialist shop is different to the mean price at the supermarket? What statistical conclusion can be made? Item Bananas Broccoli Mushrooms Nectarines Strawberries Green grapes Lettuce Potatoes Carrots Snow peas Fruit shop 1.49 2.49 4.99 3.99 2.49 9.99 1.49 2.49 1.99 11.99 4 Supermarket 2.45 3.98 7.98 5.48 3.98 4.97 0.88 2.98 1.98 9.98