1. STT 200 – L ECTURE 1, SECTION 2,4 R ECITATION 14 (12/4/2012) TA: Zhen (Alan) Zhang zhangz19@stt.msu.edu Office hour: (C500 WH) 1:45 – 2:45PM Tuesday (office tel.: 432-3342) Help-room: (A102 WH) 11:20AM-12:30PM, Monday, Friday Class meet on Tuesday: 3:00 – 3:50PM A122 WH, Section 02 12:40 – 1:30PM A322 WH, Section 04 1

2. O VERVIEW We will discuss following problems:  Chapter 23 “Inference about means” (Page 609) Nos. 5, 6, 13, 18, 21, 22 All recitation PowerPoint slides available at herehere 2

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4. Review: T distribution with degree of freedom (df) As degree of freedom (sample size-1) larger, T -> normal 4

5. Review: How to use T-table? Suppose we want to be 95% confidence about the confidence interval we construct based on a random sample with size 30. We need the T critical value with degree of freedom 30-1=29, and two-tailed since we are constructing confidence interval. 5 cum. prob t.50 t.75 t.80 t.85 t.90 t.95 t.975 t.99 t.995 t.999 t.9995 one-tail 0.500.250.200.150.100.050.0250.010.0050.001 0.0005 two-tails 1.000.500.400.300.200.100.050.020.010.0020.001 df 0.0001.0001.3761.9633.0786.31412.7131.8263.66318.31636.62 1 20.0000.8161.0611.3861.8862.9204.3036.9659.92522.32731.599 30.0000.7650.9781.2501.6382.3533.1824.5415.84110.21512.924 40.0000.7410.9411.1901.5332.1322.7763.7474.6047.1738.610 210.0000.6860.8591.0631.3231.7212.0802.5182.8313.5273.819 220.0000.6860.8581.0611.3211.7172.0742.5082.8193.5053.792 230.0000.6850.8581.0601.3191.7142.0692.5002.8073.4853.768 240.0000.6850.8571.0591.3181.7112.0642.4922.7973.4673.745 250.0000.6840.8561.0581.3161.7082.0602.4852.7873.4503.725 260.0000.6840.8561.0581.3151.7062.0562.4792.7793.4353.707 270.0000.6840.8551.0571.3141.7032.0522.4732.7713.4213.690 280.0000.6830.8551.0561.3131.7012.0482.4672.7633.4083.674 290.0000.6830.8541.0551.3111.6992.0452.4622.7563.3963.659 300.0000.6830.8541.0551.3101.6972.0422.4572.7503.3853.646 400.0000.6810.8511.0501.3031.6842.0212.4232.7043.3073.551 600.0000.6790.8481.0451.2961.6712.0002.3902.6603.2323.460 800.0000.6780.8461.0431.2921.6641.9902.3742.6393.1953.416 1000.0000.6770.8451.0421.2901.6601.9842.3642.6263.1743.390 1000 0.0000.6750.8421.0371.2821.6461.9622.3302.5813.0983.300 z0.0000.6740.8421.0361.2821.6451.9602.3262.5763.0903.291 0%50%60%70%80%90%95%98%99%99.8%99.9% Confidence Level

6. Review Try to answer following questions: 1) How to check the conditions? From which aspects? 2) How to construct the confidence interval given confidence level? 3) How to interpret the confidence interval you constructed? 4) How to interpret the phrase “with (1 - )% confidence”? Now you are ready to solve the problems. 6

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8. Chapter 23 (Page 609): #6: A random sample of 288 Nevada teachers produces the t-interval for mean salary: 38944<mean salary<42893 with 90% confidence. a) If we took many random samples of Nevada teachers, about 9 out of 10 out them would produce this confidence interval. b) If we took many random samples of Nevada teachers, about 9 out of 10 out them would produce a confidence interval that contained the mean salary of all Nevada teachers. c) About 9 out of 10 Nevada teachers earn between $38,944 and $42,893 d) About 9 out of 10 Nevada teachers surveyed earn between $38,944 and $42,893 e) We are 90% confident that the average teacher salary in the U.S. is between $38,944 and $42,893. 8

9. Chapter 23 (Page 611): #13: A histogram of body temperature for randomly selected adults. 9

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12. Chapter 23 (Page 612): #21: What are the chances your flight will leave on time? Here is a histogram and summary statistics for the percentages of flights departure on time each month from 1995 thru 2006. There is no evidence of a trend over time. (The correlation of On Time Departure% and time is r = -0.016.) 12

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14. Chapter 23 (Page 612): #22: Will your flight get you to your destination on time? Here is a histogram and summary statistics of late arrivals. There is no evidence of a trend over time. (The correlation of On Time Departure% and time is r = -0.07.) 14

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16. Thank you. 16