BUSINESS STATISTICS ASSIGNMENT
INSTRUCTIONS: ANSWER ALL QUESTIONS
QUESTION 1
i.What is the difference between point estimation and interval estimation?
ii.A sample of 8 observations has been taken from a population in which the random variable is normally distributed. The sample mean is 25 and the sample standard deviation is 5. Determine a 95% confidence interval for the population mean.
iii.The mean life of a sample of 200 light tubes produced by a company is found to be 3160 hours with a standard deviation of 180 hours. Test the hypothesis that the mean lifetime of the tubes by the company is 3200 hours.
iv.A sample of 20 measurements of the diameter of a sphere gave a mean 4.38 inches and standard deviation of 0.06 inches find
a)95% confidence limit to the actual diameter.
b)99% confidence limit to the actual diameter.
QUESTION 2
An insurance company takes a keen interest in the age at which a person is insured. Consequently a survey conducted on prospective clients indicated that for clients having the same age the probability that they will be alive in 30 years' time (2)⁄3. This probability was established using the actuarial tables. If a sample of 5 people was insured now, find the probability of having the following possible outcomes in 30 years
a)All are alive
b)At least 3 are alive
c)At most one is alive
d)None is alive
e)At least 1 is alive
f)Differentiate between Poisson and binomial probability distribution
g)Elaborate the properties of the normal distribution.
QUESTION 3
i)If 5% of the items produced turn out to be defective. Then find out the probability that out of 25 items selected at random there are
a)Exactly three defective
b)At least two defective
c)Exactly four defective
d)Find the mean and the variance
ii)Bank customer arrive randomly on a week day afternoon at an average of 3.2 customers every 4 minutes
a)What is the probability of having more than 7 customers arriving at the bank in an interval of 4 minutes?
b)What is the standard deviation of the number of customers arriving in a 4 minutes interval?
Question 4
Kathambi and company Ltd has an identical toilet soap type, but in three different wrappings. This soap is displayed for sale in three city supermarkets for five months. Use ANOVA to investigate whether or not the soap sales for each of the wrapping are equal; at 95% confidence level, using the data tabulated below
|
WRAPPING
|
|
ONE
|
TWO
|
THREE
|
|
87
|
78
|
90
|
|
83
|
81
|
91
|
|
79
|
79
|
84
|
|
81
|
82
|
82
|
|
80
|
80
|
88
|
Question 5
The following table gives the quantity supplied of a certain commodity at various prices X, holding everything else constant;
|
Y
|
12
|
14
|
10
|
13
|
17
|
12
|
11
|
15
|
|
X
|
5
|
11
|
7
|
8
|
11
|
7
|
6
|
9
|
a.Estimate the regression equation of Y on X
b.Find the coefficient of determination and explain the meaning of this coefficient.
c.Test the statistical significance of the regression at 95% confidence level, using the following information.