Test 1, / /130. MASSEY UNIVERSITY Institute of Information Sciences and Technology (Statistics)

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1 MASSEY UNIVERSITY Institute of Information Sciences and Technology (Statistics) INTRODUCTORY STATISTICS BIOMETRICS Test 1, 2003 Duration: 1 hour Questions 1 and 2 are about the following summary of the heights (in metres) of 65 men in our class: Variable Mean StDev Median Minimum Maximum Q1 Q3 Men_Heights The proportion of men in the class whose heights are between 1.80 and 1.85 is approximately a b. 0.5 c. 0.7 d e The height of the tallest man in the class was incorrectly recorded as 1.96 metres it should have been 1.90 metres. Which of the following summary statistics will not change if this value is corrected? a. mean b. interquartile range c. range d. standard deviation e. mean and standard deviation 1

2 Questions 3 and 4 relate to the following scenario. An American retailer selling software to New Zealand customers over the internet adds $US20 to the catalogue price for shipping then converts to New Zealand currency using the exchange rate $US = $NZ1.72 (in 2003). The distribution of catalogue prices in $US for software sent to New Zealand in one month has a mean of $US250 with a standard deviation $US What is the mean amount paid by New Zealanders in $NZ, rounded to the nearest dollar? a. Mean = 145 b. Mean = 156 c. Mean = 430 d. Mean = 450 e. Mean = What is the standard deviation of the amount paid by New Zealanders in $NZ? a. Standard deviation = 13 b. Standard deviation = 23 c. Standard deviation = 69 d. Standard deviation = 89 e. Standard deviation = You have calculated that the correlation coefficient between two variables is 1.3. You can conclude that a. There is a negative relationship between the variables. b. The relationship between the variables is nonlinear. c. The relationship between the variables is very strong. d. The relationship between the variables is weak. e. There has been an error in the calculations. 2

3 6. The scatterplot below describes the relationship between two variables, X and Y The correlation coefficient is approximately... a. 1.0 b. 0.8 c. 0.0 d. 0.8 e Which of the following sets of variables are examples of discrete, categorical and continuous variables? Discrete Categorical Continuous a. Maximum level of river Whether or not Rainfall (mm) in week during flood monthly temperature before flood was above average b. Number of road fatalities Number of speedcamera Money spent on road in year fines in year safety advertising in year c. Number of correct Age Whether or not the answers in a multi-choice student passed the test test d. Number of aphids counted Variety of rose Concentration of on rose bud insecticide sprayed on rose e. Number of previous Blood pressure Type of birth children of a given patient (Caesarean or natural) in a maternity unit 3

4 8. A study investigated 279 patients who had been treated for back pain. The histogram below shows the distribution of treatment costs for the patients (in dollars). What proportion of the patients had costs less than $200? a. 84 percent b. 59 percent c. 28 percent d. 11 percent e. 2 percent 9. Which of the following statements about the treatment costs for the back pain patients in Qn 8 is correct? a. The mean cost is less than the median cost. b. The median cost is less than the mean cost. c. The mean cost is a more robust description of the centre of the distribution than the median cost. d. The mean cost cannot be found for skew distributions like this. e. The median describes an economic aspect of the distribution of costs whereas the mean describes an aspect of the data that is of more social relevance. 4

5 10. The following histogram describes the heights of 200 manuka shrubs in part of the South Island of New Zealand. What have you learned about the manuka shrubs from the histogram? a. There may have been two different varieties of manuka. b. One value may have been incorrectly recorded. c. There were probably two measurements made from each shrub. d. The distribution of trunk diameters is highly skew. e. The researcher did not record information from enough shrubs. 11. The majority of the 120 members of parliament in New Zealand are aged between 40 and 60. Which of the following is a reasonable guess at the standard deviation of their ages? a. 1 b. 2 c. 5 d. 10 e. 20 5

6 Questions 12 and 13 refer to the following scatterplot matrix that shows information about five body measurements from 252 men and their percentage body fat. 12. Which variable is least closely associated with body fat? a. Age b. Weight c. Height d. Chest circumference e. Abdomen circumference 13. Which pair of variables has a negative correlation coefficient? a. Age and Height b. Height and Abdomen c. Abdomen and Fat d. Fat and Chest e. Chest and Age 6

7 Questions 14 and 15 relate to data that were collected in a study of the effect of dissolved organic matter in water in 13 lakes in northwest England. The scatterplot below shows mean dissolved organic carbon (DOC, in mg/l) and a measure of mean optical absorbance in water samples from the lakes. 14. The standard deviation of DOC is a b c d e The least squares line for predicting Absorbance from DOC is shown on the scatterplot below. Prediction of Absorbance from a lake with DOC = 2.0 would be based on the equation a. Predicted absorbance = x 2.0 b. Predicted absorbance = x 2.0 c. Predicted absorbance = x 2.0 d. Predicted absorbance = x 2.0 e. Predicted absorbance = x 2.0 7

8 16. The least squares line minimises a. the sum of squares of perpendicular distances from points to the line b. the sum of squares of vertical distances from points to the line c. the sum of squares of horizontal distances from points to the line d. the sum of squares of the fitted values e. the effect of outliers 17. The following frequency table describes the distribution of ages of the 430 Full Professors in a US university. Age Frequency Under to to to Which of the following stacked bar charts best displays this distribution? Under to to to 80 a b c d e 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 8

9 18. The stacked bar charts below show the age distributions for the ranks Instructor, Assistant Professor and Associate Professor in the same US university as described in Qn 17. Under to to to 80 Assoc Prof Assist Prof Instructor 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% What is the best conclusion to draw from the diagram? a. There are more Associate Professors than Instructors b. There are fewer Associate Professors than Instructors c. Associate Professors tend to be younger than the other groups d. Associate Professors tend to be older than the other groups e. Just under half of those aged over 50 are Associate Professors 19. Computer enhancements of graphical displays, such as 3-dimensional bar charts a. help to convey the signal better b. avoid non-data noise c. introduce non-data noise d. (a) and (b) e. should be used sparingly 9

10 20. The diagram on the right was published in The Dominion on October 24, The diagram is misleading. Four of the following statements are true. Which one is false? a. The areas corresponding to Tax and GST are a greater proportion of the total area than their share of the price, making the reader think that they are too high. b. The amounts for the last two categories are rounded to the nearest cent, making them appear smaller than values with one decimal place. c. The petrol nozzle is non-data noise that does not add to the information in the display. d. A pie chart would show the data more clearly and fairly. e. Shading should have been added since a 3-dimensional object is being used to represent the total price. WHO GETS WHAT FROM 90.9c A LITRE PRODUCT COST 26.9c TAX 32.2c GST 10.1c OVERHEADS/WHOLESALE MARGIN/INCOME TAX 14c RESELLER 7c LOCAL BODY TAX 0.7c Source: Mobil 10