L19SamplingDistMean

# L19SamplingDistMean - MGT 2250 —— Lesson 19 The...

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Unformatted text preview: MGT 2250 —— Lesson 19 The Sampling Distribution of the Mean March 9, 2011 Deﬁnition: The sampling distribution of the mean is the probability distribution of all possible sample means (y) of sample size n that could be drawn from a population. I. ) Sampling error: The absolute value of the difference between a sample mean (KEEN) or standard deviation ( g ) and the t1 ue population mean i )or standard deviation( m. Example: WV”: \$111111 11151111 11111111111 ”A" :f: 4i 1- 1 “‘5‘ “N i“ 51 1 11 13:1 1 «111 1 1 a 3 ~“ (“3 2‘1?) ,1 firm” "‘1 Eidlnxi’sjké ”@7951 K "‘1 WWW 3 \$1111.13} 11’3““117111g 1 33mm 11.1.1 1 :2” W ‘ Q4111 ”1.9% {111‘ g (1.71/9 _! (”ﬁg/ﬁg 11W (25W; wﬁgyﬂlﬁﬁ Eff-"31111911111?” ”{5}? g; Q 12 L71 6‘1: W123 5 Lgmm 1wﬁgﬁﬁgeé Q19 ﬁe W'Vn 3 M 11. e 11 £1 1% @1513 % Siﬂww‘ﬁg “ﬂ g: 2.} Paint asti1nates~1he sample mean (X ) is a point estimate of the pggﬂggﬁgﬂ mgﬁg_(qm l The gamnlp ei’anrlard damn/111913 ( “hf \; is 3”: 11113111 estimate 1111111 p11 efinlation standard 11111111111111 { gm ). >2“ “*1 31"; 91111 1 1341111 5% 1:1 L 1 gSanlpDistribMean u 1 ~ 3.) Developing the sampling distribution: Example: EAE Corporation i2\$ FREQUENCY DISTRIBUTION OF A FROM 5“ 30 SDVIPLE RANDOM SAMPLES~§ o1: 300 EAI MANAGERS . 9 Mean Annual Salary (39) Frequency Relative Frequency 49,500 00 49 999 99 2 .004 ‘1 50 ,000 0.0 50 499 99 16 .032 , 50,500 00450, 999 99 52 .104 A 51,000 00 51 499 99 2,13,, 101 , .202 ”A 51 ,500 00~51 ,999 99 / 2 ”32:7 ‘1’ 133 229.91 52,000. 00 52 ,499 99 {EB .220 ," 52,500; 004299999 . 54 1108 1' 59000002252499.99 25 .052 ,‘ 53,500.00—25399999 6 .012 ,5 W- J Totals 500 1.000 LiQSampDisU‘ibMean - 7 - 4.) Properties of the samﬂiingjiistribution. W/‘M (4;, 65) The“€entraiLimit Theorem” C: 5;“ 5‘ \ If the sample size n is sufﬁeientﬁy large (generaléy greater mag: er , ”K equai 4w 3%) the}; ihe summing ﬁisérébﬁééen wiﬁ appreximaie 3: Emmiai W ,7” ﬁistributien no matter the ghape 0f the pepuiation. The larger the H, the mere “normaﬁly” distributed the sampﬁing éistributiem beeemee. L 1 98ampDistri'bMean (K, '2 La) 7.) Example Problems: EAI Corporation If the mean salary for the population of managers is known to be \$51,750 with a standard deviation of \$4000: a) What is the probability of drawing a s ple of 50 managers from this population with a sample mea \ withi\$~ \$500 of the population E1 25 mean? "fL-‘Ww rkuﬁﬂff 73%” k43r~u ////i::‘ “:”“\x ””‘ xx“ * y” , it ”:2 2: 31:35} as 5/3 / é: :1 f3“ 1 '" c U // ﬁéf’? ~g// gﬂw Q? a W a L/ t b) If the sample size were increased to (1‘00, what would this probability a i .1 m. be . ‘ /”““M“;i/L:gr ”X“ f? g E K} k‘f‘Lf/ﬂ‘x m , ,,,,, 7 l , E l\\ 3 «vi» No éﬁmw a. l a, ,zg « ~: a u % ~—- L-I ' t“ t” ' ‘1 / W? A W' """" ﬂ@@&/\\k WW“ <Mﬂ MM/ \ g *% ‘W%WW§? \\\ Q 5%n} :2 M W w M g; o l i ‘32», x f p" m I? wwwwww m M; ‘ L; U (/2 é—~ WWW, W” thigfflﬁw’w W , ﬁ 6 a MWWﬁMW %- a _9Wm l _ ...... it ----- e} if the sample size were mortgaged to 35, what wouid this probability 3 he? Ll 9SampDistribMean ...
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