QUANTITATIVE FINANCE

Quantitative Finance and Financial Markets

Quantitative Finance and Financial Markets

Question #2

Perform the following two tailed hypothesis test using a .05 level of significance

Intrinsic by gender

State the null and alternate hypothesis for the test

Use Microsoft excel to process your data and run the appropriate test. Copy and paste the result of the output to your report in Microsoft Word

Identify the significance level, test static, and the critical value

State whether you are rejecting or failing to reject the null hypothesis statement.

Explain how the results could be used y the manager of the company.

Solution

Gender selected = 1 (Male)

Null hypothesis, Ho: µ= 5.0 and Alternate hypothesis, Ha: µ= 5.0

Level of significance = 0.05

Test used is z-test for population mean

Critical scores are z=1.96 and z=-1.96

Rejection rule is: reject Ho if z calculated is >1.96 or <-1.96

Test static is z = (x-bar- µ)/(s/vn) = (5.06-5.0)/(1.0309/v52) = 0.419

Decision: since 0.419<1.96, we fail to reject Ho

Conclusion: there is not sufficient evidence that mean intrinsic score for males is different from 5.0

Z Test of Hypothesis for the Mean

Data

Null Hypothesis m=

5

Level of Significance

0.05

Population Standard Deviation

1.03

Sample Size

52

Sample Mean

5.06

Intermediate Calculations

Standard Error of the Mean

0.1429601

Z Test Statistic

0.419

Two-Tail Test

Lower Critical Value

-1.959963985

Upper Critical Value

1.959963985

p-Value

0.674709

Do not reject the null hypothesis

(Data collected for the analysis can be seen from the appendix)

The fact that mean intrinsic satisfaction rating for men is not different from 5 is encouraging. A right tailed test would have been more appropriate but two tailed test also serves the purpose. The manager should try to retain this level of satisfaction among the male employees.

i.

Country

Score

Japan

87.1

ii.

Country

Score

Swaziland

48.5

iii.

U.K.

U.S.A.

82.4

81.3

iv.

From the z-score indices of United Sates and United Kingdom, it can be said that United Sates of America has the highest female status as the life expectancy at birth for women, maternal mortality ratio, the percentage of women in parliament and women's economic activity rate in USA is high.

b.

The z-score of the of the index that is life expectancy at birth for women, maternal mortality ratio, the percentage of women in parliament and women's economic activity rate, is a measure of the dispersion of data. Some data are quite dispersed, as shown on the left graph, where the values for individuals may be quite different from each other. Other data are not very dispersed, as shown on the right graph, meaning that the values for individuals are quite similar to each other.

Question 3

a.

i. Highest female status

Region

Score

Asia

87.1

ii. Lowest female status

Region

Score

Africa

48.5

b.

c.

From the above, it can be said that the female status in most of the different regions are same in terms of life expectancy at birth for women, the percentage of women in parliament, maternal mortality ratio and women's economic activity rate. The reason of this statement is that; although the female status varies in some regions, but overall the female status is similar in most of the regions.

Question # 5

Perform the following two-tailed hypothesis test, using a .05 significance level:

Extrinsic variable by Position Type

State the null and an alternate statement for the test

Use Microsoft Excel (Data Analysis Tools) to process your data and run the appropriate ...