Intro to Inference Lecture 1

Transcription

1 Supported by TLRI Grant Intro to Inference Lecture 1 Statistics Department University of Auckland New Zealand C7, S1 Aucklanders lack spend in sustenance average but of five sure minutes make up doing for it their in style hairnz in Herald the 25/8/98 morning compared Auckland with three women minutes spend six minutes applying makeup, two for people in the other minutes cities. longer They than women also in spend six minutes Wellington getting and dressed, Dunedin. But Christchurch women take the two minutes longer make-up than cake, people at eight in minutes. Aucklanders are less likely to have Christchurch h h and Dunedin. Aucklanders spend more time in brushing their hair and dressing in the morning than people in the other main cities, and they have least time left for breakfast. The vanity jibes from people south of the Bombays have been borne out in a Sanitarium Health Food survey of 100 people in Auckland, Wellington, Dunedin and Christchurch. Aucklanders spend an average of five minutes doing their hair in the morning compared with three minutes for people in the other cities. They also spend six minutes getting dressed, two minutes longer than people in Christchurch. breakfast only 61% do so, compared with 83% of Wellington folk. And, of course, darlings, Aucklanders prefer coffee to tea to kick-start the day. The survey launches a new liquid Sanitarium breakfast, which the company says has the same nutritional value as two Weet-Bix and milk so busy commuters can drink on the run. C7, S2 Aucklanders lack in sustenance but sure make up for it in style Aucklanders spend more time in brushing their hair and dressing in the morning than people in the other main cities, and they have least time left for breakfast. The vanity jibes from people south of the Bombays have been borne out in a Sanitarium Health Food survey of 100 people in Auckland, Wellington, Dunedin and Christchurch. Aucklanders spend an average of five minutes doing their hair in the morning compared with three minutes for people in the other cities. They also spend six minutes getting dressed, two minutes longer than people in Christchurch. NZ Herald 25/8/98 Auckland women spend six minutes applying makeup, two minutes longer than women in Wellington and Dunedin. But Christchurch women take the make-up cake, at eight minutes. Aucklanders are less likely to have breakfast only 61% do so, compared with 83% of Wellington folk. And, of course, darlings, Aucklanders prefer coffee to tea to kick-start the day. The survey launches a new liquid Sanitarium breakfast, which the company says has the same nutritional value as two Weet-Bix and milk so busy commuters can drink on the run. The vanity jibes from people south of the Bombays have been borne out in a Sanitarium Health Food survey of 100 people in Auckland, Wellington, Dunedin and Christchurch. C7, S3 Aucklanders lack spend in sustenance average but of five sure minutes make up doing for it their in style hairnz in Herald the 25/8/98 morning compared Auckland with three women minutes spend six minutes applying makeup, two for people in the other minutes cities. longer They than women also in spend six minutes Wellington getting and dressed, Dunedin. But Christchurch women take the two minutes longer make-up than cake, people at eight in minutes. Aucklanders are less likely to have Christchurch h h and Dunedin. Aucklanders spend more time in brushing their hair and dressing in the morning than people in the other main cities, and they have least time left for breakfast. The vanity jibes from people south of the Bombays have been borne out in a Sanitarium Health Food survey of 100 people in Auckland, Wellington, Dunedin and Christchurch. Aucklanders spend an average of five minutes doing their hair in the morning compared with three minutes for people in the other cities. They also spend six minutes getting dressed, two minutes longer than people in Christchurch. breakfast only 61% do so, compared with 83% of Wellington folk. And, of course, darlings, Aucklanders prefer coffee to tea to kick-start the day. The survey launches a new liquid Sanitarium breakfast, which the company says has the same nutritional value as two Weet-Bix and milk so busy commuters can drink on the run. C7, S4 1

2 On American passenger ships, expand- ing will be forcing forced to reduce the capacity. authorities into said the action. change could add several C7, S5 will be The forcedunited to reduce capacity. States Coast said Guard the change has could add several Coast raised Guard spokeswoman its average Lisa Novak. passenger weight from 72.5kg to 84kg. It likely is tothe capsize. first time it Thehas Federal done Transit Administration, so since the with 1960s. C7, S6 it is a blow to many commercial boat The operators, United States Coast who Guard will has be Administration forced to has reduce raised its average 72.5kg capacity. to 84kg. It is the first time it has will be forced to reduce capacity. said the change could add several C7, S7 The Federal Transit Authority, with doneresponsibility so since the 1960s. for the nation s company that buses, conducts ocean still burials, is portlier tests than 50 vehicles years ago may as not if come the to average raise prices. Anticipating rider i less usable many weighs commercial68kg. boat operators, It has whoproposed charters in fivea states, jump Ken to Shortridge will be forced to reduce capacity. 79kg. said the change could add several C7, S8 2

3 Prompted by a 2003 plane crash in as anorth huge surprise Carolina, but it is athe blowfederal to space onaviation many of the 50 boats he will be Administration forced to reduce capacity. has raised said the its change average could add several weight estimate from 77kg to near The 86kg. Coast Guard has followed the lead C7, S9 as a huge surprise but it is a blow to many commercial boat operators, who will be forced to reduce capacity. space on many of the 50 boats he charters in five states, Ken Shortridge said the change could add several The company Coast Guard has that followed conducts the lead He ocean said overloaded burials, boats are more is concerned the new rules will force responsibility them for to the raise nation sprices. buses, still C7, S10 Ken Shortridge said the change could add several hundred dollars to the cost of each will be forced to reduce capacity. said the change could add several C7, S11 Actual weight (kg) Ideal weight (kg) M 110 Gender Fastest speed driven (km/h) C7, S12 3

4 distribution (predicted) What is the average weight of this population of 521 male Stage 1 University of Auckland Statistics students? Weight (kg) C7, S13 C7, S14 What is the median weight of this population of 521 male Stage 1 University of Auckland Statistics students? X = weight Pop. median? (521 Male Stage 1 Stats students) C7, S15 C7, S16 4

5 X = weight Pop. median? (521 Male Stage 1 Stats students) n = 9 Simple random sample of 9 students whose weights (in kg) are: 70, 52, 63, 70, 81, 71, 57, 62, 67 Od Ordered dweights: 52, 57, 62, 63, 67, 70, 70, 71, 81 C7, S17 C7, S18 X = weight Pop. median? (521 Male Stage 1 Stats students) n = 9 estimate median = 67kg Interpretation: The population median weight is about 67kg C7, S19 Interpretation: The population median weight is about 67kg Weakness: All estimates are uncertain What shall we do about this? Give a range or interval of believable values for the population median (which we call an uncertainty interval or uncertainty band ) C7, S20 5

6 C7, S21 C7, S22 Interpretation: The population median weight is about 67kg Weakness: All estimates are uncertain What shall we do about this? Give a range or interval of believable values ( uncertainty interval or uncertainty band ) How shall we do this? Treat the sample as if it were the population Re-sample from the sample, with replacement We call this bootstrapping C7, S23 Bootstrapping From the original sample, randomly sample (with replacement) until the re-sample size equals the original sample size Calculate the median of the re-sample (bootstrap sample) Do many re-samples Use the medians of the re-samples to calculate an interval that has a good chance of containing the population median C7, S24 6

7 Bootstrapping Original sample: Distribution of re-sample medians kg median = 67kg My re-sample: kg kg Re-sample median = C7, S25 C7, S26 X = weight n = 9 Pop. median? estimate Bootstrap confidence interval Original sample median = 67kg Bootstrap confidence interval: (, ) (521 Male Stage 1 Stats students) Interpretation: We estimate that the population median weight is somewhere between and C7, S kg C7, S28 7

8 will be The forcedunited to reduce capacity. States Coast said Guard the change has could add several Coast raised Guard spokeswoman its average Lisa Novak. passenger weight from 72.5kg to 84kg. It likely is tothe capsize. first time it Thehas Federal done Transit Administration, so since the with 1960s. C7, S29 Why does this method work so well? Link _to _pdf C7, S30 Aucklanders lack spend in sustenance average but of five sure minutes make up doing for it their in style hairnz in Herald the 25/8/98 morning compared Auckland with three women minutes spend six minutes applying makeup, two for people in the other minutes cities. longer They than women also in spend six minutes Wellington getting dressed, and Dunedin. two But Christchurch women take the minutes longer than make-up people cake, in at eight minutes. Aucklanders are less likely to have Christchurch h h and Dunedin. Aucklanders spend more time in brushing their hair and dressing in the morning than people in the other main cities, and they have least time left for breakfast. The vanity jibes from people south of the Bombays have been borne out in a Sanitarium Health Food survey of 100 people in Auckland, Wellington, Dunedin and Christchurch. Aucklanders spend an average of five minutes doing their hair in the morning compared with three minutes for people in the other cities. They also spend six minutes getting dressed, two minutes longer than people in Christchurch. breakfast only 61% do so, compared with 83% of Wellington folk. And, of course, darlings, Aucklanders prefer coffee to tea to kick-start the day. The survey launches a new liquid Sanitarium breakfast, which the company says has the same nutritional value as two Weet-Bix and milk so busy commuters can drink on the run. C7, S31 Time to do hair (Aucklanders) X = time Pop. average? (Aucklanders) n = 100 Estimate = 5 mins C7, S32 8

9 Time to do hair (Aucklanders) X = time n = 100 Pop. average? Estimate = 5 mins (Aucklanders) What should we do now??? C7, S33 C7, S34 9