Question 1

a)Refer to the paragraph below and answer the following question.

A researcher wants to study about the Body Mass Index (BMI) of students in UNITAR International University (UNITAR). The researcher divided the BMI according to 5 categories: severely underweight, underweight, normal, overweight and obesity. Due to large number of students in UNITAR, only 500 respondents were selected in the study to represent all students. Result from the study indicates that 9% students were severely underweight, 20% students were underweight, 31% of students is in the normal category, 25% students were overweight and 15% were obesity.

i.What is the population and sample used in this study? (1 Mark)

ii.Determine the type of variable being studied by the researcher. (1 Mark)

iii.Determine the level of measurement for the variable under study. (1 Mark)

iv.What is the type of statistic used in this research? Explain your answer. (2 Marks)

b)Given a set of data as follows:

90, 72, 84, 91, 67, 332, 88, 75, 76, 80

Based on the data set:

i.Compute the mean, median and mode. (3 Marks)

ii.Which measure of central tendency that is suitable to represent the data. Explain your answer. (2 Marks)

(Total: 10 Marks) Question 2

a) Table 1 represent the monthly rainfall data distribution in Shah Alam.

Table 1

Rainfall (inches)

Number of Month

20 - 24

12

25 - 29

38

30 - 34

55

35 - 39

84

40 - 44

52

45 - 49

20

50 - 54

0

55 - 59

15

i. Determine the relative and cumulative frequency for the data.

(2 Marks)

ii. Determine the standard deviation for the data set.

(4 Marks)

iii. Draw a histogram for the data set.

(4 Marks)

(Total: 10 Marks)

Question 3

a) Table 2 shows results from a survey for married adults classified by social status and level of happiness.

Table 2

Social status

Level of happiness

Happy

Not happy

High

150

26

Average

120

34

Low

185

65

i.What is the probability that a married adult is happy?(2 Marks)

ii.What is the probability of selecting a married adult who is high social status or those who are not happy? (2 Marks)

iii.What is the probability of selecting a married adult who is happy given that they are from average social status? (2 Marks)

b) A normal probability distribution has a mean of 70 with a standard deviation of 10. Find the probability of value:

i. between 52 to 68.

(2 Marks)

ii. between 55 to 77.

(2 Marks)

(Total: 10 Marks)

Question 4

a)The Medical Rehabilitation Education Foundation reports that the average cost of rehabilitation for stroke victims is RM24,672. To see if the average cost of rehabilitation is different at a large hospital, a researcher selected a random sample of 25 stroke victims and found that the average cost of their rehabilitation is RM25,226 with the standard deviation of RM3,251. At = 0.01, can it be concluded that the average cost at a large hospital is different from RM24,672?

Answer the following questions based on the information above.

i.State the null and alternative hypothesis for this problem. (1 Mark)

ii.What is the critical value for this test? Sketch a diagram showing the rejection region for this critical value. (2 Marks)

iii.Calculate the test statistics for this problem. (2 Marks)

iv.Based on your answer in (ii) and (iii), what is your decision and conclusion for the problem? Explain your answer. (2 Marks)

b)The president of a large university wishes to estimate the average age of the students presently enrolled. From past studies, the standard deviation is known to be 2 years. A sample of 50 students is selected, and the mean is found to be 23.2 years.Find the 95% confidence interval of the population mean.(3 Marks)

(Total: 10 Marks) Question 5

Peter obtained cash from ATM machine. He suspects that the rate at which he spends cash is affected by the amount of cash he withdrew at his previous visit to an ATM machine. To investigate this, he deliberately varies the amount he withdraws. He recorded the amount he withdraws (in RM) and the number of hours (in hour) until his next visit to an ATM machine. The data is tabulated as in Table 3.

Table 3

Amount withdraw (RM)

Number of hours

400

56

100

62

1000

200

1100

300

1200

100

1500

250

200

48

900

180

a) Determine the independent and dependent variable.

(2 Marks)

b) Find the regression line.

(6 Marks)

c) Determine the number of hours until his next visit to an ATM machine if Peter withdraw

RM2000. (2 Marks)

(Total: 10 Marks)