1. Claims department of an insurance firm audited 150 customers' payment claims. Out of these, 12% were found to be defective.
i. Estimate the standard error of the proportion of defective parts.
ii. Construct the 99% confidence interval for the proportion of defective parts.
2. The following table shows classifications of workers in an insurance firm, according to the disciplinary action taken by the management and their promotional experience.
Promotional experience
|
Disciplinary action
|
Promoted
|
Not promoted
|
|
Offenders
|
30
|
670
|
|
Non offenders
|
70
|
230
|
Test whether the disciplinary action taken and promotional experience are associated. Use 0.01 level of significance.
3. An economic review press hypothesizes that the average life of its largest web press is 45,000 hours, they know that the standard deviation of the press life is 2100 hours. From a sample of 36 press, the company finds a sample mean of 1,300 hours. At 0.01 should the company conclude that the average life of the press is less than the hypothesized 45,000 hours?
4. A vegetable vendor buys cabbages at Ksh. 70 and sells at Ksh. 100 each. Because it is a perishable commodity, all the cabbages left unsold at the end of the day get rotten. Analysis of his sales records over the last 50 days produced the frequency distribution as shown in the table below.
|
Cabbages sold
|
10
|
11
|
12
|
13
|
14
|
|
No. of days
|
4
|
10
|
14
|
16
|
6
|
Determine the optimum stock level which the vendor should hold based on expected monetary value. [8 Marks]
5. Differentiate between the following terms:
i. Statistic and parameter
ii. One-tailed test and two-tailed test
6. A nutritionist claims that at most 40% of the residents of slums in Nairobi do not eat a balanced diet meal in a day. A random sample of 400 slum dwellers was taken out, of whom 178 were found not to have been eating a balanced diet. Test whether this claim is significantly low at the 5 % significance level?
7.
a) Portfolios may be held by individual investors and/or managed by financial professionals, hedge funds, banks and other financial institutions. It is a generally accepted principle that a portfolio is designed according to the investor's risk tolerance, time frame and investment objectives. Elaborate on this statements.
b) State and explain two main factors influencing the efficiency of a portfolio
8. The table below shows the possible returns of two assets, X and Y together with their probabilities:
|
Probability
|
0.2
|
0.2
|
0.2
|
0.2
|
0.2
|
|
Return of x (%)
|
11
|
9
|
25
|
7
|
-2
|
|
Return of y(%)
|
-3
|
15
|
2
|
20
|
6
|
Required:
i) Compute the expected return of each Asset
ii) Compute the variance and standard deviation of each asset
iii) Determine the expected return and standard deviation of a portfolio composed of 60% investment in X and 40% investment in Y. Compute the coefficient of correlation between the returns of X and Y, interprete the results.
iv) a) Compute the expected return and standard deviation of a portfolio formed between X and Y if the following investment proportions were used:
|
Proportion of X (%)
|
100
|
75
|
50
|
25
|
0
|
|
Proportion of Y (%)
|
0
|
25
|
50
|
75
|
100
|
c) Plot a graph of expected portfolio return against portfolio standard deviation