Statistical Analysis for Desklib

STATISTICS
STUDENT NAME/ID
[Pick the date]

Question 1
(a) Null hypothesis H0: Hair colour and regional promotions are independent.
(b) Alternative hypothesis H1: Hair colour and regional promotions are dependent.
(c) The Type I error for this test is 5% which implies that there is a 0.05 probability that a true
null hypothesis may be rejected. This implies that even if statistical analysis suggests that the
complaints are valid, there is a 5% chance that the complaints may not be valid and the same
needs to be considered.
(d) The Type II error for this test would refer to a situation when the null hypothesis is indicated
to be true when it is false. For the company, it would describe a situation when even though
the allegations or complaints may be rejected but they may be valid. Hence, this error needs
to be minimised.
(e) Critical value of the test statistic
Chi square test statistic would be appropriate measured for the present case.
Degree of freedom = (n-1) (r-1) = (4– 1) (6-1) = 15
Level of significance = 0.05
The critical value of the chi square statistic = 24.9957
(f) The calculated value of test statistic
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Sum of all the chi-square calculation values would be the chi-square statistic.
Calculated value of chi square statistic = 47.0367
(g) The p value for this would be based on the degree of freedom and chi-square statistic.
Degree of freedom = (n-1) (r-1) = (4 – 1) (6-1) = 15
The p value = 0.00
The p value represents the probability that a chi-square statistics would have 15 degree of
freedom which is more extreme than 47.0367. Further, if the p value is lesser than level of
significance then the rejection would be incurred for null hypothesis.
(h) The p value is lower than level of significance (0.00<<0.05) and therefore, the null
hypothesis would be rejected and alternative hypothesis would be accepted. Therefore, the Hair
colour and regional promotions are dependent.
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(i) It is apparent that regional promotions seem to be linked to colour and hence a thorough
review of these promotions need to be conducted with focus on performance so as to make
necessary changes. Also, a strict action must be taken against those managers who have
discriminated.
Question 2
(a) Null hypothesis H0: Distribution of demographics of total sales force and regional
promotions are independent.
(b) Alternative hypothesis H1: Distribution of demographics of total sales force and regional
promotions are dependent.
(c) The Type I error for this test is 5% which implies that there is a 0.05 probability that a true
null hypothesis may be rejected. This implies that even if statistical analysis suggests that
discrimination has been observed, there is a 5% chance that the company should not be
accused by ACLU with regards to practising discrimination.
(d) The Type II error for this test would refer to a situation when the null hypothesis is indicated
to be true when it is false. For the company, it would describe a situation when even though
the allegations or complaints may be rejected but they may be valid. As a result, the company
should conduct an internal enquiry even if ACLU rejects the discrimination charges.
(e) Expected number of promotions
Expected frequency
Total number of promotions = 400
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