STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

More documents

Recommendations

Info

Examples on working with proportions, prepared for STAT170 workshop at Numeracy Centre, Macquarie University, by Nan Carter from various sources. CATEGORICAL VARIABLE with ONLY TWO CATEGORIES. 4. A manufacturer claims that 95% of the components supplied for a new jet transport meet a specified rigid standard of performance (ie 5% do not). A sample of 400 of the components is tested, and 30 do NOT meet the performance standard. Comment on the manufacturer’s claim. 5. A report claims that the percentage of miscarriages among LSD users is 12%. From the files in the maternity ward of a Sydney hospital, out of 100 pregnant women who used LSD, 24 had miscarriages. Comment on the claim made in the report 6. The president of a certain company believes that 30% of the company’s orders come from new or firsttime customers. In a random sample of 100 orders, 40 are from new customers; does this meet the company’s claim? CHECKS: Q1 z=2.294 Q2: z = 3.693; Q3: z = 2.182; Now we want to do the same questions using χ 2 . The problem is how to set up the hypothesis H0, and how to find values for the expected numbers E. Try thinking of it this way: we are often interested in • testing a theory which is used to give the hypothesis H0 and the expected numbers if the hypothesis is true. • testing a ‘claim’ made by others, and which is used to give the hypothesis H0 and the expected numbers 36 Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.
if the hypothesis is true. FOR EXAMPLE: In a study of the genetics of eye colour in fruit flies, there is a theory that the numbers of red-eyed and whiteeyed flies will be in the proportions of 1:3. So we have H0: the proportions are as 1:3 (i.e ¼ are red-eyed and ¾ white-eyed) If the total number of flies is 9693, we can find the expected numbers in each class, assuming H0 is true. Expected values are 1/4 x 9693 = 2423.25 and ¾ x 9693 = 7269.75. The data supplies the observed numbers (1981 and 7712 respectively), and so we can calculate 37 χ 2 = Σ[(O-E) 2 /E] where the sum is over all cells, and degrees of freedom = no of classes – 1 χ 2 = (1981-2423.5) 2 /2423.25 +(7712-7269.75) 2 /7269.75 = 107.6 with 1 df. From χ 2 table, p-value < 0.05, so we reject H0 and conclude that the theory does not hold for the inheritance of red and white eyes in these fruit flies. In the population from which this sample was taken, there are fewer red-eyed and more white-eyed flies than the theory claims. 4. Do the above exercise using a different statistical test. 5. In tossing a die 300 times the frequency of occurrence of 1, 2, 3, 4, 5, 6 are, respectively, 43, 49, 56, 45, 66 and 41. • Is there any basis for the claim that the die is biased? If there is a bias, which number appears more frequently than expected? 6. In a survey taken 5 years ago, 25% of students watched less than 5 hours of TV per week, 10% watched 20 or more hours per week, and the rest watched Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.
Page 1 and 2: STAT170 Workshop Notes prepared by
Page 3 and 4: Week 4 H/Y. Exercises for STAT170 w
Page 5 and 6: Week 5 H/Y. Questions on SAMPLING D
Page 7 and 8: EXAMPLES ON WORKING WITH PROPORTION
Page 9 and 10: EXERCISE 4. Suppose we wanted to pl
Page 11 and 12: We now have a single sample of diff
Page 13 and 14: Week 8 H/Y. STAT170 workshop on the
Page 15 and 16: Week 9 H/Y. Stat170 workshop on Hyp
Page 17 and 18: EXERCISE 11: In Q5 use a hypothesis
Page 19 and 20: PAIRED t-TEST: QUESTION 1. (from St
Page 21 and 22: QUESTION 4. “You can taste the lu
Page 23 and 24: sp =√[{(n1-1)s1 2 + (n2-1)s2 2 }
Page 25 and 26: a) Draw the scatterplot of the data
Page 27 and 28: Residual 20 15 10 5 0 -5 -10 -15 -2
Page 29 and 30: Residual Residual 1 0.8 0.6 0.4 0.2
Page 31 and 32: Relation: Monthly sales volume outc
Page 33 and 34: Unstandardized Residual 33 40 20 0
Page 35: mid-year exam paper (See below: the
Page 39 and 40: sandwich, only 4 became ill. We wou
Page 41 and 42: Notice that a) 3.89 = 1/0.26, so if

STAT170 Workshop Notes prepared by Nan Carter for Numeracy ...

Create successful ePaper yourself

Delete template?

Save as template?