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Page 1 of 8 U NIVERSITY OF T ORONTO Q UANTITATIVE M ETHODS IN E CONOMICS II ECMB12H3F (LEC02) M ID - TERM T EST S OLUTIONS D URATION : 90 MINUTES O CTOBER 20, 2010 I MPORTANT : (i) This test should be answered in BALLPOINT PEN and students who attempt the test in pencil would surrender their rights to request for re-assessment. (ii) Ensure HANDWRITING is LEGIBLE and show STEP-BY-STEP CALCULATIONS . Answer all questions only in the DESIGNATED PAGES . ROUGH WORK should be done in the LAST TWO PAGES and contents in those pages will not be graded. (iii) AIDS ALLOWED a HAND-WRITTEN SINGLE-SIDED LETTER SIZE CRIB SHEET (photocopies or printed copies not allowed) and a NON-PROGRAMMABLE CALCULATOR (other electronic devices with calculator functions not allowed). (iv) DO NOT SEPARATE any page from this test. Student Name Student ID# Question 1 2 3 4 5 Total Marks 17 31 20 12 20 100 Score
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Page 2 of 8 1. As the vice president in operations of a major fast food chain, the current average time to serve a customer using the drive-thru service is 3 minutes and you are interested in cutting down the average time by installing a new automated self-serve system, which costs millions of dollars. The new system has been tested in a particular location where it served a sample of 64 customers and the average time is 2.75 minutes with a standard deviation of 1 minute. (i) Follow the six-step critical value approach to hypothesis testing at 5% level of significance with the sample data to determine whether to invest in this new automated self-serve system or not. (ii) Can you determine the range of the -value of the test statistic? (i) 12 marks and (ii) 5 marks (i) Step 1 the company will only invest in the new automated self-serve system if it can significantly reduce the average time to serve customers using the drive-thru service, which implies a one tail test. and Step 2 the level of significance is 5% and the sample size . Step 3 only the -test is appropriate where there is no information about the population variance. Step 4 for and with degrees of freedom , the critical value for the one tail test is . Step 5 with sample statistics , , and . The test statistic Step 6 since and it is less than the critical value of , the test statistic falls in the rejection region and hence the null hypothesis is rejected. There is enough evidence to conclude that the average time to serve a drive-thru customer is significantly less than 3 minutes and hence it is worthwhile to invest in the new automated self-serve system.
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