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# INTRO TO STATISTICS 1 STA 2023

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This 12 page Class Notes was uploaded by Golden Bernhard on Friday September 18, 2015. The Class Notes belongs to STA 2023 at University of Florida taught by Maria Ripol in Fall. Since its upload, it has received 45 views. For similar materials see /class/206569/sta-2023-university-of-florida in Statistics at University of Florida.

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Date Created: 09/18/15

Review Chapter 8 c1 and Sig Testsrnr p and prpzllsingthel 1 Why tin we use the 1 table 2 What assumptlnns dnwe need tn make Random Samples Cheek speclflc assumpuon forthat test 0 Use the must restrictive nne far all eases and anI will he nk one Sample Proportron c1 rsample slze mustbe at least equal to 5 one Sample Propomon ST 7 musthave at least ten sueeesses and ten fal ures Two Sample Proporuon c1 eboth sample slzes must be atleast ual to 10 Two Sample Propomons ST 7 atleast 5 sueeesses and 5 fallures must m eaeh ofthe samples 3 Which estimatnr nfp tin we use N X 2 P a one Sample Propomon Con dence Interval n 4 X p 7 a one Sample Propomon Slgnlflcance Test n X 1 Two Sample Propomon Con dence Interval quotl 2 N X2 1 F2 i n r12 Two Sample Propomons Slgnlflcance Test 4 Make and interpret c1 and ST 5 Read Minltah Output 5 Interpret Results Examples For each of the following examples we will rst determine which kind of problem it is Then we will set the problem up as if to do by hand We will interpret the Minitab output given for each problem 1 Suppose that in a random sample of 50 babies conceived by an in vitro fertilization process test tube babies 35 are girls Does this sample evidence show convincingly that the in vitro process favors the female gender Explain 0 Which kind of problem is this 0 Interpret the results of the Minitab output from the last page 2 Four sets of identical twins were selected at random One child was selected at random from each pair to form an quotexperimental groupquot these four children were sent to school The other four children were kept at home as a control group At the end of the school year the IQ scores presented below were obtained Does this eVidence justify the conclusion that lack of school experience has a depressing effect on IQ scores Experimental Control Pair Group Group A 1 10 11 1 B 125 120 C 139 128 D 142 13 5 0 Which kind of problem is this 0 Interpret the results of the Minitab output from the last page 3 A restaurant has recently started using a dessert cart that is pushed around the eating area for diners to view and it is hoped be unable to resist On the rst ten evenings the cart was used the average expenditure per night for desserts was 130 compared to an average of 110 prior to the use of the cart The standard deviation for the ten evenings was 65 Does it look like the cart will improve sales signi cantly 0 Which kind of problem is this 0 Interpret the results of the Minitab output from the last page 4 A social scientist believes that the fraction of Republicans in favor of the death penalty is greater than the fraction of Democrats in favor of the death penalty She asked random samples of 200 Republicans and 200 Democrats and found 46 Republicans and 34 Democrats favoring the death penalty Do these data support the social scientist s belief 0 Which kind of problem is this 0 Interpret the results of the Minitab output from the last page 5 The effect of alcohol consumption on the body appears to be much greater at high altitudes than at sea level To test this theory a scientist randomly selects 12 subjects and randomly divides them into two groups of siX each One group is transported to an altitude of 12000 feet where each subject ingests a drink containing 100 cc of alcohol The second group receives the same drink at sea level After two hours the amount of alcohol in the blood grams per 100 cc for each subject is measured The data are shown in the table Do the data provide sufficient evidence to support the theory that retention of alcohol in the blood is greater at high altitudes Sea Level 12000 Feet 007 013 010 017 009 015 012 014 009 010 013 014 0 Which kind of problem is this 0 Interpret the results of the Minitab output from the last page Test and Confidence Interval for One Proportion Test of p 05 vs p gt 05 Exact X N Sample p 950 CT P Value 35 50 0700000 0553918 0821382 0003 Test and CT for One Proportion Sample X N Sample p 950 CI 1 37 54 0685185 0544476 0804761 Paired T Test and Confidence Interval Paired T for exp control N Mean StDev SE Mean exp 4 12900 1467 control 4 12350 1034 517 Difference 4 550 500 250 95 CT for mean difference 246 134m T Test of mean difference 0 vs gt0 T Value 220 P Value 0058 T Test of the Mean Test of mu 1100 vs mu gt 1100 Variable N Mean StDeV SE Mean T dessert 10 1300 653 206 097 018 T Confidence Intervals Variable N Mean StDev SE Mean 950 CT dessert 10 1300 653 206 8331767 Test and Confidence Interval for Two Proportions Sample X N Sample p 1 46 200 0230000 2 34 200 0170000 Estimate for p1 p2 006 95 CT for p1 p2 00181778 0138178 Test for p1 p2 0 vs gt 0 Z 150 P Value 0066 Test and CI for Two Proportions Sample X N Sample p 1 47 202 0232673 2 35 202 0173267 95 CT for p1 p2 00188205 0137632 Two Sample T Test and Confidence Interval Two sample T for sea level vs 12000ft N Mean StDeV SE Mean sea leve 6 01000 00219 00089 12000ft 6 01383 00232 00095 95 CT for mu sea leve mu 12000ft 00678 0008 T Test mu sea leve mu 12000ft vs lt T 294 P 00082 DE 7 9 Review of Statistical Inference from STA 2023 Con dence Intervals and Signi cance Tests for one mean matched paired differences difference of two independent means one proportion difference of two independent proportions Chapter 7 CI and Signi cance Tests for means using the t distribution 1 Why do we use the t table 2 What assumptions do we need to make How do we check them Random Samples Population is Normal 3 Find Formulas on tables Con dence Interval Signi cance Test H0 Ha TS pvalue 4 Read Minitab Output 5 Interpret Results CI does NOT include from H0 gt Supports Ha pvalue small gt Supports Ha Examples For each of the following examples we will rst determine which kind of problem it is Then we will set the problem up as if to do by hand We will interpret the Minitab output given for each problem 1 D0 pregnant women who use cocaine have babies with lower birth weight than women who do not use cocaine Pregnant women were tested for cocainecrack and the birth weights of babies in grams were recorded and averaged for women who tested positive and those who tested negative separately n S I 2 Positive Test 134 2733 599 Other 5974 3118 672 2 Many children are diagnosed each year with asthma In an effort to educate these children about their condition an educational Video was developed To test the effectiveness of this Video ten randomly selected children of elementary school age who had been recently diagnosed were chosen to participate in a study A nurse asked the children a series of questions about asthma then showed them the Video and asked the questions again The children s scores follow Child 1 2 3 4 5 6 7 s 9 10 Before I 61 60 52 74 64 75 42 63 53 56 After I 67 62 54 83 60 89 44 67 62 57 3 A news report states that over 70 of mail received by a household in a week is advertisements A sample of 20 households produced the following data adV mail adV 12 16 0750000 18 24 0750000 15 24 0625000 15 25 0600000 21 33 0636364 21 24 0875000 17 22 0772727 20 27 0740741 16 28 0571429 13 19 0684211 20 25 0800000 20 23 0869565 17 20 0850000 13 20 0650000 23 33 0696970 15 28 0535714 9 12 0750000 18 30 0600000 9 14 0642857 24 35 0685714 TwoSample TTest and Cl Sample N Mean StDev SE Mean 1 134 2733 599 52 2 5974 3118 672 87 Difference mu 1 7 mu 2 Estimate for difference 7385000 95 CI for difference 7488738 7281262 TiTest of difference 0 V5 lt TiValue 7734 PiValue 0000 DE 140 Paired TTest and Cl before after Paired T for before 7 after ean StDev SE Mean before 10 600000 100000 31623 after 10 645000 132267 41826 Difference 10 7450000 512619 162104 95 CI for mean difference 7816705 7083295 TiTest of mean difference 0 V5 lt 0 TiValue 7278 PiValue 0011 OneSample T adv Variable N Mean StDev SE Mean 95 C1 adv 20 168000 42501 09503 148109 187891 OneSample T mail Variable N Mean StDev SE Mean 95 C1 mail 20 241000 62061 13877 211955 270045 OneSample T acv Variable N Mean StDev SE Mean 95 C1 D V 20 0704315 0098776 0022087 0658086 0750543 SE Mean Variable N Mean e T P D V 20 0704315 0098776 0022087 020 0424

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