X=o 90% C. I d=o I 99% C- I 95% C- I =) given

Size: px

Start display at page:

Download "X=o 90% C. I d=o I 99% C- I 95% C- I =) given"

Linda Flynn
5 years ago
Views:

1 3 ' Math 150 Lecture Notes Date Z 005 =164 Z 001 =33 Z 005 =196 Z 0005 =58 : Norm X=o Confidence Intervals for µ ( known ) Procedure 90% C I d=o I 99% C- I 95% C- I =) X=o 01 X= 005 Step 1: Find / Z / Step : Find E = Z / p n en % Margin of Error Step 3: Find given given X ± E Step 4: Write X E<µ<X + E Ex: A study of 36 taxi drivers shows that the average time they wait for a customer is 65 minutes with a standard deviation of 10 minutes n=36 I= 65 0=10 a) Find a 95% confidence interval for the true waiting time of all " " X=O 05 taxi drivers are 95% You stepe : E = =196 that Confident the real waiting fine is Step : E=Zazfu= =3 between 6 and Steps : I IE stcp4 : 617<µ<68@ 68 minutes 1

2 b) Find a 99% confidence interval for the true waiting time of all a- taxi drivers 001 [ STAT ][ TESTS ] Step : E = 0005 Zo oos= : Z Interval Steps : E= -58 = 43 step } : I ± E I : 65 Step 4 : 6o7<µ<69@ Explain lnpt : Data [ stats ] 0:10 n : 36 C- level : 099 ftpojgtjb#output c) What happens the interval as gets smaller? Explain The Interval getswider Ex: Dr # wants to find out the average number of hours that students spend doing Mathematics homework per week He conducts of survey of 144 students The average is 7 hours and the standard deviation is 5 hours a) Find a 99% Confidence interval for the real number of hours that students study per week? Calculator ( ) Dr V is 99 to sore that students study between 65 65<µ<7@ And 7- T hrs per week

3 b) Juan claims that he studies on average 14 B hours per week Is that reasonable? NO because 14 Is outside the interval 9 Z / Sample Size: n = E E= ZEE rn E= Zxz : -58 8=5 n=( 581 ) z = 104=10 people 3

4 73 Confidence Intervals for p Procedure Step 1: Find / Z / I : Step : Find E = Z / r ˆp(1 ˆp) n Step 3: Find ˆp ± E t ˆp = x n X±E " " # of YES Step 4: Write ˆp E<p<ˆp + E I m I Ex: Nacho is interested in finding out the percentage of Angelinos that believe in the existence of Santa Claus He conducts of survey with 00 people of which 140 said that they believe in the existence of Santa Claus n= 00 11= =07 00 a) Find a 90% confidence interval for the true proportion of Angelinos that believe in the existence of Santa Claus 010 Sl ) = =1-64 nacho is goio Confident sz ) E= 164*70*0054 that between 65% and 537 P^±E 071= ) O646cpcotn#f 75% of Angeline > believe in Santa 4

5 } b) Find a 95% confidence interval for the true proportion of Angelinos X=O 05 that believe in the existence of Santa Claus 15=0-7 Sl ) Xz =196 [ STAT ] [ TEST ] 5 ) E= = 0063 A : 1 Prop Z Int 00 Xi ) n : Loo PIE 07 I ) O63t<p<0# Explain? - C- level : 095 c) How large of a sample is needed in order to have a % margin of error? n=(tee)pc p F=o -7 E= 40=00 tonsil a6 n =L's )( ono = 0168 = 017 whole # 5

6 7 Confidence Intervals for µ ( unknown ) T-Distribution Zz t d f=n - l d f Find the following critical values (a) t 0050 n=1 : =1-96 (b) t = 181 (c) t 0005 = 819 (d) t = 650 6

7 level Procedure Step 1: Find / t / Step : Find E = t / S pn Step 3: Find X ± E Step 4: Write X E<µ<X + E Ex1: The Mayor of Los Angeles wants to estimate the true average salary of city employees: A survey of 5 employees had a mean of $19 with a standard deviation of $5 Find a 95% confidence interval for the true mean salary h = 5 I=19 5=5 se ) E = 005 to -054=064 The mayor 5 ) EI 064 X=oO5_ 53 ) IIE 94 ) 19+- = 064= 95% sure that city make employees between $17 and 174 $1 hour [ STAT ][ TEST ) 8 : Tinterval per is I : : C : 7

8 a - Ex: For the following data: Find a 99% confidence interval for the mean X= 583 5=17 n=g :( Calculator 867 ) ftpggg ] n= 6 54 )99<µ<8#f Ch3= X= 001 [ STAT ] [ EDIT ] [ STAT ][ CALC ] - 1 : WARS stats you qqio sure that people make $3 and $9 a month 8

9 74 Confidence Intervals for -Distribution Find the following critical values XR 1-05 (a) in X[=Xo q = 7516=6908 XI 1/= (b) =8845 o = xinioasiioiino 00 (c) ftpqqk =

10 1) Procedure Step 1: Find / R = / Step : Find L = 1 / Step 3: Find (n 1)S R < < (n 1)S L Ex1: Use the following data to find a 95% confidence interval for the true standard deviation n =1 S =7 =005 Sl ) X }z= 1/0050 = ) X{ = 1/09+50 = ) C n - 5 < o< cry xs ( 0 ) ( 49 ) 0 < 0 < ( 0 ) ( 49 ) < 101 < # 535<0<1 Explain : 10

11 aqs 01 Ex: For the following data: Find a 99% confidence interval for the variance I = 583 5=17 X=o n= 6 51 ) 1/00055=16750 = XR= 57 XI = Xo 5= (5) ( 1 7) 1 < 0<(53*041 O8b7<0<35#_ 11

Problems Pages 1-4 Answers Page 5 Solutions Pages 6-11

Part III Practice Problems Problems Pages 1-4 Answers Page 5 Solutions Pages 6-11 1. In estimating population mean or proportion what is the width of an interval? 2. If 25 college students out of 80 graduate