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Grade-12 Math Studies   Revision worksheet on Statistics                                        Date:4^th Oct -2010
1.	The Type Fast secretarial training agency has a new computer software spreadsheet package. The agency investigates the number of hours it takes people of varying ages to reach a level of proficiency using this package. Fifteen individuals are tested and the results are summarised in the table below.
Age | 32 | 40 | 21 | 45 | 24 | 19 | 17 | 21 | 27 | 54 | 33 | 37 | 23 | 45 | 18
(x) | | | | | | | | | | | | | | |
Time | | | | | | | | | | | | | | |
(in hours) | 10 | 12 | 8 | 15 | 7 | 8 | 6 | 9 | 11 | 16 | t | 13 | 9 | 17 | 5
(y) | | | | | | | | | | | | | | |
(a)	(i)	Given that S_y = 3.5 and S_xy = 36.7, calculate the product-moment correlation coefficient r for this data.
(4)
(ii)	What does the value of the correlation coefficient suggest about the relationship between the two variables?
(1)
 
(b)	Given that the mean time taken was 10.6 hours, write the equation of the regression line for y on x in the form y = ax + b.
(3)
 
(c)	Use your equation for the regression line to predict
(i)	the time that it would take a 33 year old person to reach proficiency, giving your answer correct to the nearest hour;
(2)
(ii)	the age of a person who would take 8 hours to reach proficiency, giving your answer correct to the nearest year.
(2)
(Total 12 marks)

2.	Ten students were asked for their average grade at the end of their last year of high school and their average grade at the end of their last year at university. The results were put into a table as follows:
Student | High School grade, x | University grade, y

1
2
3
4
5
6
7
8
9
10

90
75
80
70
95
85
90
70
95
85

3.2
2.6
3.0
1.6
3.8
3.1
3.8
2.8
3.0
3.5

Total | 835 | 30.4
 
(a)	Given that s_x = 8.96, s_y = 0.610 and s_xy = 4.16, find the correlation coefficient r, giving your answer to two decimal places.
(2)
 
(b)	Describe the correlation between the high school grades and the university grades.
(2)
 
(c)	Find the equation of the regression line for y on x in the form y = ax + b.
(2)
(Total 6 marks)

3.	A shopkeeper wanted to investigate whether or not there was a correlation between the prices of food 10 years ago in 1992, with their prices today. He chose 8 everyday items and the prices are given in the table below.
| sugar | milk | eggs | rolls | tea bags | coffee | potatoes | flour
1992 price | $1.44 | $0.80 | $2.16 | $1.80 | $0.92 | $3.16 | $1.32 | $1.12
2002 price | $2.20 | $1.04 | $2.64 | $3.00 | $1.32 | $2.28 | $1.92 | $1.44

(a)	Calculate the mean and the standard deviation of the prices
(i)	in 1992;
(ii)	in 2002.
(4)
 
(b)	(i)	Given that s_xy = 0.3104, calculate the correlation coefficient.
(ii)	Comment on the relationship between the prices.
(4)
 
(c)	Find the equation of the line of the best fit in the form y = mx + c.
(3)
 
(d)	What would you expect to pay now for an item costing $2.60 in 1992?
(1)
 
(e)	Which item would you omit to increase the correlation coefficient?
(2)
(Total 14 marks)

4.	Several candy bars were purchased and the following table shows the weight and the cost of each bar.
| Yummy | Chox | Marz | Twin | Chunx | Lite | BigC | Bite
Weight (g) | 60 | 85 | 80 | 65 | 95 | 50 | 100 | 45
Cost (Euros) | 1.10 | 1.50 | 1.40 | 1.20 | 1.80 | 1.00 | 1.70 | 0.90
 
(a)	Given that s_x = 19.2, s_y = 0.307 and s_xy = 5.81, find the correlation coefficient, r, giving your answer correct to 3 decimal places.
(2)
 
(b)	Describe the correlation between the weight of a candy bar and its cost.
(1)
 
(c)	Calculate the equation of the regression line for y on x.
(3)
 
(d)	Use your equation to estimate the cost of a candy bar weighing 109 g.
(2)
(Total 8 marks)

5.	Tania wishes to see whether there is any correlation between a person’s age and the number of objects on a tray which could be remembered after looking at them for a certain time.
She obtains the following table of results.
Age (x years) | 15 | 21 | 36 | 40 | 44 | 55

Number of objects
remembered (y)

17

20

15

16

17

12

(a)	Use your graphic display calculator to find the equation of the regression line
of y on x.
(2)
(b)	Use your equation to estimate the number of objects remembered by a person aged 28 years.
(1)
(c)	Use your graphic display calculator to find the correlation coefficient r.
(1)
(d)	Comment on your value for r.
(2)

(Total 6 marks)