University of Malawi
BAF, BCTM, BCME, BAC, BAM, BAU & BBA
Business Statistics: Test #3 (Groups)
Attempt ALL questions September 10, 2021 Max of 4 hours
1. The distributions of income in some Third World countries are considered wedge
shaped (many very poor people, very few middle income people, and even fewer
wealthy people). Suppose we pick a country with a wedge shaped distribution and
observe that the average salary is K200,000 per year with a standard deviation of
K800,000.
a) How is it possible for the standard deviation to be greater than the average?
(2 marks)
b) What is the probability that the average income of 1,000 residents from the country
will be between K200,000 to K210,000 (7 marks)
c) Find the 60th percentile for the average incomes of samples of size 1,000?
(5 marks)
2. Suppose that an accounting firm does a study to determine the time needed to complete
one person’s tax forms. It randomly surveys 100 people. The sample mean is 23.6
hours. There is a known population standard deviation of 7.0 hours. The population
distribution is assumed to be normal.
a) Construct a 90% confidence interval for the population mean time to complete the
tax forms. (5 marks)
b) Construct a 98% confidence interval for the population mean time to complete the
tax forms. (5 marks)
c) Explain why the confidence interval in part b) is larger than the confidence interval
in part a). (3 marks)
d) Give an interpretation of what the interval in part b) means. (2 marks)
3. A survey estimates with 90% confidence that the mean monthly household income in
the Malawi falls between K69,720 and K69,922. Find the
a) point estimate for mean household income (3 marks)
b) margin of error for the mean household income (EBM). (3 marks)
4. The average height of young adult males has a normal distribution with standard
deviation of 2.5 inches. You want to estimate the mean height of students at your
university to within one inch with 93% confidence. How many male students must you
measure? (4 marks)
5. A particular brand of tires claims that its deluxe tire averages at least 80,000 km before
it needs to be replaced. From past records of the performance of the tires, the standard
deviation is known to be 12,000 km. A sample of 28 deluxe tires fielded a mean lifespan
of 46,500. Using α = 0.05, is the data highly inconsistent with the claim? Assume the
population was normally distributed. (7 marks)
6. The mean number of sick days an employee takes per year is believed to be about 10.
Members of a HR personnel department do not believe this figure. They randomly
survey eight employees. The number of sick days they took for the past year are as
follows: 12, 4, 15, 3, 11, 8, 6, 8. The personnel department requested you to test the
belief at 𝛼 = 0.05. (14 marks)
7. Your statistics instructor claims that 60 percent of the students who take her Elementary
Statistics class go through life feeling more enriched. For some reason that she can't
quite figure out, most people don't believe her. You decide to check this out on your
own. You randomly survey 64 of her past Elementary Statistics students and find that
34 feel more enriched as a result of her class. Test at 𝛼 = 0.05 the claim by the statistics
instructor. (7 marks)
8. The Center for Disease Control (CDC) reports that the mean life expectancy is different
between middle class and lower class adults in Africa. Suppose that you randomly
survey death records for people in the CDC death record population. Of the 124 middle
class, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the
82 lower class, the mean life span was 34.1 years with a standard deviation of 15.6
years.
a) Conduct a hypothesis test to see if the mean life spans in the country were the same
for middle class and lower class adults at 𝛼 = 0.10. (7 marks)
b) What type of error is likely to have occurred after the hypothesis test? (2 marks)
End of Paper
