1.1 Table 1.1 below gives the Marks obtained by 200, first Year Statistics students at

Regent Business School in the 2017 year end examinations.

Table 1 Statistics Marks of first year student at Regent Business School

Classes No of Students

0 >10 10

10>20 20

20>30 25

30>40 15

40>50 20

50>60 35

60>70 45

70>80 10

80>90 15

90>100 5

Using the grouped data in Table 1.1 calculate:

1.1.1 Calculate the mean number of marks. (2)

1.1.2 Calculate the median number of marks. (4)

1.1.3 Calculate the modal number of marks. (4)

1.1.4 Calculate the standard deviation. (5)

1.2 Using data in Table 1.1 above construct an upward sloping ogive and indicate the

value of the upper quartile (q3) on the graph (5)

QUESTION TWO [20]

2.1 A collage that specializes in training people for top-level management positions

administers various types of physical and psychological tests. In one such test,

objects must be assembled and pictures arranged in order. Although the maximum

possible score for this test is 130, the college has found that results in the past have

followed an approximately normal distribution with a mean of 91.7 and the standard

deviation of 6 minutes.

Calculate the percentage of people who obtain scores in the following ranges.

2.1.1 Above 105 (2)

2.1.2 Above 83 (2)

2.1.3 between 80 and 100 (3)

2.1.4 below 74 (3)

2.2 Good Samaritan Hospital keeps records of Emergency Room traffic. Those records

indicate the number of patients arriving between 18h00 and 19h00 has a Poisson

distribution with parameter = 6.9. Determine the probability that on a given day the

number of patients who arrive at the emergency room between 18h00 and 19h00 will

be:

2.2.1 Exactly 4 (2)

2.2.2 between 4 and 10 inclusive (4)

2.3 According to the Daily Racing Form, the probability is about 0.67 that the favorite in a

horse race will finish in the money(first, second ,or third place).In the next five races,

what is the probability that the favorites horse finishes, between two and four time,

inclusive. (4)

QUESTION THREE [20]

3.1 A national survey was conducted to obtain information on the alcohol consumption

patterns of South African adults by marital status. A random sample of 1772

residents 19 years old and older yielded the data displayed in Table 3.1

Abstain 1-60 Over 60 Total

Single 67 213 74 354

Married 411 633 129 1173

Widowed 85 51 7 143

divorced 27 60 15 102

Total 590 947 225 1772

Test at 5% level of significance if there is sufficient evidence to conclude that an

association exits between marital status and alcohol consumption. (10)

3.2 Iron is essential to most forms and to normal human physiology. It is an integral part

of many proteins and enzymes that maintain good health. Recommendations for iron

are provided in dietary reference intake, developed by Institutes of the National

Academy of Sciences. The recommended dietary allowance (RDA) of iron for adult

females under the age of 51 is 18 milligrams (mg) per day. Table 3.2 presents iron

intakes, in milligrams, were obtained during a 24-hours period for 45 randomly

selected adult females under age of 51.

15.0 18.1 14.4 14.6 10.9 18.1 18.2 18.3 15.0

16.0 12.6 16.6 20.7 19.8 11.6 12.8 15.6 11.0

15.3 9.4 19.5 18.3 14.5 16.6 11.5 16.4 12.5

14.6 11.9 12.5 18.6 13.1 12.1 10.7 17.3 12.4

17.0 6.3 16.8 12.5 16.1 14.7 12.7 16.3 11.5

At the 1% significance level, do the data suggest that adult females under the age of

51 are, on average, getting less that the RDA mg of 18 mg of iron? Assume that the

population standard deviation is 4.2 mg.

QUESTION FOUR [20]

In an attempt to analyze the relationship between advertising and sales, the owner of a

furniture store recorded the monthly advertising budget (in thousand rand) and the sales (in

millions rand) for a sample of 12 months. The data is listed below.

Advertising sales

23 9.6

46 11.3

60 12.8

54 9.8

28 8.9

33 12.5

25 12.0

31 12.0

36 11.4

88 12.6

90 14.4

99 15.9

3. 1 Identify the dependent and the independent variables. (1)

3. 2 Draw a scatter diagram for the above data. Does it appear that adverting and

sales are linearly related? (4)

3. 3 Calculate Pearson's correlation coefficient and interpret it. (5)

3. 4 Calculate the (least square) regression line and interpret the coefficients

(Intercept and the slope). (8)

3. 5 Estimate the sales if the company spends R150 000 on advertising. (2)

QUESTION FIVE [20]

5.1 The average price of a 30 cm ruler, a 5 cm eraser, an HB pencil and a black felt-tip

pen were recorded in both 2007 and 2017 as below. (Prices are in R.)

2007 2017

Item Price (R)

Number sold

(in millions)

Price (R)

Number sold

(in millions)

Ruler 17 7.5 23.7 8.2

Eraser 7.3 4.2 12.5 5.1

Pencil 5.5 12.6 8.7 13.5

Pen 15.8 8.5 22.9 9.5

5.1.1 Find the Laspeyres price and quantity indices for 2017 using a base year of

2007. (4)

5.1.2 Interpret the values in 5.1.1 above. (4)

5.2 The following data refer to the number of visitors (in thousands) that visited the

uShaka water world in the years 2015-2017.

I

Jan-Apr

II

May-Aug

III

Sep-Dec

2015 - 86 98

2016 84 91 106

2017 86 104 139

You are required to:

5.2.1 Obtain a 3-term moving average trend. (4)

5.2.2 Find the seasonal variations using the additive model. (8)