FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
Private Bag 13388, Windhoek, Namibia
Phone: +264 (61) 207 2781
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MATHEMATICS, STATISTICS AND ACTUARIAL SCIENCE DEPARTMENT
BASIC BUSINESS STATISTICS 1B (BBS112S)
ASSIGNMENT 1
SEMESTER 2, 2023
QUESTION 1 [22 MARKS]
1.1
A random sample of employees of a large company was asked the question, "Do you participate
in the company's stock purchase plan?" The answers are shown below.
Yes
No
No
Yes
No
No
Yes
Yes
No
No
No
Yes
Yes
Yes
No
Yes
No
No
Yes
Yes
No
Yes
Yes
No
Yes
Yes
No
Yes
Yes
Yes
Yes
No
No
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Use a 90% confidence interval to estimate the proportion of employees who do not participate
in the company's stock purchase plan.
1.2
[6]
A student calculates a 90% confidence interval for the population mean when population
standard deviation is unknown, and the sample size is 9. The confidence interval is -24.3
cents to 64.3 cents. Find the sample mean.
1.3
[3]
The lifetime of a light bulb is normally distributed with the mean 3000 hours and a variance of
1392 hours. A simple random sample of 36 bulbs is taken.
(a) What is the expected value, standard error, and shape of the sampling
distribution of x ?
[3]
(b) What is the probability that the average lifetime in the sample will be between 2670.56 and
2809.76 hours?
[5]
(c) How large of a sample needs to be taken to provide a 0.01 probability that the average
lifetime in the sample will be greater than 3219.24 hours?
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[5]
QUESTION 2 [23 MARKS]
2.1
The personnel department of a large corporation wants to estimate the family dental
expenses of its employees to determine the feasibility of providing dental insurance
plan. A random sample of 10 employees reveals the following family dental expenses (in N$)
for the past year.
110
362
246
85
510
208
173
425
316
179
(a) Find the mean point estimate for the employees’ dental expenditure in the past year. [3]
(b) Compute a 95% confidence interval for the true population mean in the employees’ dental
expenditure.
2.2
[5]
An advertising agency that serves a major radio station wants to estimate the mean
amount of time that the station’s audiences spend listening to the radio daily. The agency
wanted to be 95.76% confident of being correct within + or – 5 minutes. If the sample size
needed was 220 audiences, estimate the standard deviation used.
[5]
~~END OF ASSIGNMENT 1~~
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