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

More documents

Recommendations

Info

Question 3. A certain bank has many branches throughout Australia. The age of the branch managers of a random sample of 156 of these branches is given as follows: Age Frequency 30-34 8 35-39 21 40-44 24 45-49 32 50-54 40 55-59 23 60-64 8 Give a graphical summary for these data. CHECK ANSWERS: 1.a) • Popln: All registered medical practitioners in the Sydney Metropolitan Area • Sample: the 50 randomly selected names • Variable: annual incomes • Type of data: continuous (numerical) 1.b) • Popln: all residents in NSW • Sample: 200 blood donors from all major cities • Variable: major blood grouping • Type of data: categorical, nominal (A,B,AB,O) 1.c) • Popln: days of production • Sample: the 21 days for which data were collected • Variable: the number of defectives found • Type of data: numerical, but is it ordinal or continuous? 1.d) • Popln: all couples married for 10 years • Sample: 25 such couples • Variable: number of children in the family • Type of data: categorical, ordinal 1.e) • Popln: adults residing in Sydney • Sample: 75 males and 75 females registered to vote • Variables: income and sex • Type of data: continuous for income and binary for sex. Question 2. a): histogram, boxplot, stem and leaf b): barchart (or pie chart) c): barchart or histogram d): barchart e): comparative boxplot Question 3. Histogram. 2 Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.
Week 4 H/Y. Exercises for STAT170 workshop held at Numeracy Centre, Macquarie University; prepared by Nan Carter. Wk4_5h Observations on many variables are ‘normally distributed’ (the histogram is close to being symmetrical, and has one hump, is unimodal). We can relate the area under a curve between any two values of the variable to the probability of a random value occurring by chance. This concept of relating the probability of a value occurring by chance and the area under a curve, is used for other distributions e.g. the ‘tdistribution, the chi-square distribution. By convention, the symbol z is used for a variable that is normal, with mean zero and standard deviation 1. N(0,1) is the ‘standard normal variable’. Suppose we have a normal distribution with mean μ = 10, and standard deviation σ = 2. What is the probability that a value, x, selected at random from the population, will be: a) between 7 and 14? b) between 12 and 15? c)less than 6.5?; c) equal to 15 or more extreme? 1. a) If 37.7% of a normal population has a standard score between zero some positive z-value, find that z-value. b) what is the probability that a z-score will lie between zero and 1.16? c) what is the probability that a randomly chosen z-score will lie between zero and 1.16? In the following questions, use the table of single-tail areas for the standardised normal curve that is given in your study guides and textbook. Y is the symbol for the normal variable. 3. If μ = 5, σ = 1 and z = 2.05, what is the value of y? and if probability, p, is 0.02, what is the value of z? 4. Let μ = 150 and σ = 24 a) if p = 0.0188, what is z? b) if z = -1.25, what is y? b) if z = 0.42 what is p? c) what is the probability of a value of z that is more extreme than z = -2.08? Finding the probability that a value could be more extreme than a given value is used in testing nhypotheses. 5. If the probability that a box of kiwi fruit is underweight is 0.1992, how many underweight boxes would you expect in a consignment of 150 boxes? If the probability were 0.0150, how many would you expect? 6. a) what is the probability of a value of z that is more extreme than z = -1.43? b)If z = 0.71, what is p? c)What is the area under the curve between z = -1.43 and z = 0.71? d) If the area under the curve in the upper tail is 0.22, what is the value of z? 7. a) If z = 1.00 what is p? b) If p = 0.03, what is the value of z? 3 Nan Carter: workshop notes prepared for Numeracy Centre Macquarie University.
Page 1: STAT170 Workshop Notes prepared by
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 and 36: mid-year exam paper (See below: the
Page 37 and 38: if the hypothesis is true. FOR EXAM
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?