QUESTION ONE

a) A population has a mean of 100 and variance of 81. A random sample size of 25

is collected.

i. What is the mean and standard deviation of the sampling distribution?

[4 marks]

ii. What is the probability that the sample mean is greater than 102? [5 marks]

b) An administrator for a private hospital believes that of all patients, 30% will

generate bills that become at least 2 months overdue. A random sample of 200

patients is taken. What is the probability that the sample proportion is between

0.27 and 0.33? [6 marks]

c) Monthly rates of return on the shares of a particular common stock traded on

Lusaka Stock Exchange (LUSE) are independent of one another and normally

distributed with a standard deviation of 1.6. If a sample of 12 months is taken, what

is the probability that the sample standard deviation is less than 2.5? [5 marks]

[TOTAL: 20 MARKS]

QUESTION TWO

a) A random sample of 15 employees of airtel call Centre was taken and each employee

took a competency test. The mean of the scores achieved by these employees was

56.3 with a standard deviation of 7.1. Results of this test have been found to be

normally distributed in the past. Construct a 95% confidence interval for the mean test

score of all the employees of the call Centre. [6 marks]

b) Find a 95% confidence interval estimating the mean height of the 1500 female students

at UNILUS by taking a sample size 100. (Assume the mean of the sample is 67.45 and

that the standard deviation on the sample is 2.93). [5 Marks]

c) A study of a sample of 110 supermarkets reveals that 31 offer carrier bags suitable to

shoppers. Construct a 95% interval estimate of the proportion of all supermarkets that

have these carrier bags. [

i. How many supermarkets would have to be included in the sample if the

confidence interval of the proportion of establishments with carrier bags has

to be within 5% of the actual population proportion with a 95% level of

confidence. [4 marks]

[TOTAL: 20 MARKS]

QUESTION THREE

a) Banting is believed to reduce weight when done for a minimum of 10 days. A

random sample of 5 ladies were weighed before and after Banting. The data is

displayed on a table below.

Person Weight before Weight After

1 85 82

2 96 90

3 105 95

4 78 90

5 120 110

Construct a 95% for the difference in mean weight. [8 Marks]

b) Suppose you want to know the internet speed of two different mobile networks.

Network X Network Y

Sample size 12 15

Sample Mean 25 19

Sample std dev 60 50

Assuming that the population is normally distributed with equal variances.

Construct a 95% for the difference in mean internet speed. [6 Marks]

c) In a random sample, 70 of 100 men and 16 of 50 women are professional

footballers. Form a 90% confidence interval for the difference between the

proportion of men and the proportion of women who are professional footballers.

[6marks]

[TOTAL: 20 MARKS]

QUESTION FOUR

a) You are the manager of Hungry Lion. You want to determine whether the mean

waiting time to place an order has changed in the past month from its previous

mean value of 4.5 minutes. Assuming that the population is normally distributed,

with a population standard deviation of 1.2 minutes. You select a sample of 25

orders during a one-hour period with a sample mean of 5.1 minutes. Test this at

0.05 level of significance. [8 Marks]

b) The manufacturers of chicco biscuits are particularly concerned that the mean

weight of a chicco biscuits is not greater than 6.03 grams. A sample of 50 chicco

biscuits is selected; the sample mean is 6.034 grams, and the sample standard

deviation is 0.02 grams. Using =0.01 level of significance, is there evidence that

the population mean weight of the chicco biscuits is greater than 6.03 grams?

[6 marks]

c) KFC has developed a new process to ensure that orders at the drive-through are

filled correctly. The business problem is defined as determining whether the new

process can increase the percentage of orders processed correctly. The previous

process filled orders correctly 85% of the time. Data are collected from a sample

of 100 orders using the new process. The results indicate that 94 orders were filled

correctly. At the 0.01 level of significance, can you conclude that the new process

has increased the proportion of orders filled correctly? [6 marks]

[TOTAL: 20 MARKS]

QUESTION FIVE

a) Suppose the manager of Orca deco resigned and three sales people at the branch

are being considered for the position. All three have about the same length of

service, education and so on. In order to make a decision, it was suggested that

each of their monthly sales are shown in Table 1. The "treatments" in this problem

are sales people

Monthly Sales (K '000')

At the 0.05 significance level, is there a difference in mean sales? [10 Marks]

b) Four groups of students were subjected to different teaching techniques and

tested at the end of a specified period of time. As a result of dropouts from the

experimental groups (due to sickness, transfer, and so on), the number of students

varied from group to group. Do the data shown below present sufficient evidence

to indicate a difference in the mean achievement for the four teaching techniques?

Use 0.05 level of significance.

A B C D

65 75 59 94

67 69 78 89

73 83 67 80

79 81 62 88

81 72 83

69 79 76

90

454 549 425 351

[10 Marks]

[TOTAL: 20 MARKS]

END OF ASSIGNMENT

Mr. Amos Mr. Bright Ms. Collins

25 25 19

15 15 17

14 17 13

10 16 11

21 17 12

Sample 17

Mean

18 14.4