It can be concluded that both distributions of COST and SIZE of all the companies is positively skewed, that is, they are skewed right.From table 2 above, it can be seen that the medium industry risk category has the highest average cost while the low industry risk category has the lowest average cost. However, the low industry risk category has the largest average size while the high industry risk category has the highest average size.
shows that companies with a medium priority on use of analytics in managing risks have the highest average cost of 12.40. On the other hand, companies with a low priority on the use of analytics in managing risks have the lowest average cost of 6.06. However, in terms of the average size of a company, companies with a low priority on the use of analytics in managing risks have the highest average size unlike those with a high priority which have the lowest average size.
it can be seen that the distribution is positively skewed. Consequently, there were presence of outliers as seen in figure 1 at 4013 and figure 2 at points beyond 2801.stem and leaf plot in part a, it can be seen that there were 7 outliers.
It can be seen that the low industry risk category has the largest distribution of size of companies while the high industry risk category had the lowest. Consequently, low industry risk had the highest interquartile range while the high risk industry had the lowest interquartile range. On the other hand, the medium risk category has the highest mean industry size while the high category had the lowest. The results therefore confirm that the highest industry size is found in the low industry risk category while the high risk category has the lowest.
It can be seen in figure 4 that most of the companies are in the low risk industry with a representation of 82% (n = 69). They are followed by the medium risk industry (15%, n = 11) and then lastly the high risk industry (3%, n = 2). However, most companies are in the medium analytical risk category with a representation of 70% (n = 51). The rest of the companies are equally distributed in the high and low analytical risk with a representation of 15% (n =11) apiece.From the scatterplot in figure 5 above, it can be seen that there is a negative relationship between the cost and size of the company.
For a joint probability, event A and event B occur simultaneously while in a relative joint probability, event B occurs given event A has occurred.
P (A) = 1
P (A and B) = P(A)×P(B)= 0.0137
P (A|B) = P (A and B)/P(B)
= 0.0137 / 0.0274
The probability of selecting a firm that places a medium importance on analytics or operates in a low risk industry is:
P = AUB
Thus, 0.1507 + 0.1507 = 0.3014
- The confidence interval suggests that 71.63 ± 1.7129, which is equal to the range 69.92 and 73.34.
The p-value to confront the hypothesis Ho : µ = 70 against Ha : µ ≠ 70 would be less than 5%. From the z-score calculator given the confidence interval is 1.7129, the derived p-value will be 0.04.
The multiple linear regression model bests predict the dependent variable performance. The conclusion is based on the fact that the multiple linear regression has the highest adjusted R square of 0.551 compared to the linear simple regression of 0.464.Origin is not a significant variable since it has a p-value of 0.9 which is greater than 0.05.
The final regression model has a coefficient of determination of 0.56. Consequently, the adjusted coefficient of determination if 0.55. Thus, 55% of the variability in the model is explained by factors within the model while 45% is explained by factors not in the model.
It is also evident that the constant performance is -2.92 keeping all factors constant. A unit increase in salary leads a 0.11 unit increase in performance keeping all factors constant. On the other hand, a unit increase in years of experience leads to a 0.12 unit increase in performance keeping all factors constant.
H0: Proportion of managers recruited form outside the company is equal to 50%
H1: Proportion of managers recruited from outside the company is lower than 50%
Number of external managers = 62
Total number of managers = 150
Proportion = 62/150 = 0.413
H0: P = 50%
H1: P < 50%
Alpha = 0.05
Z = 1.96
Std error = SQRT (0.413*(1-0.413)/150) = ± 0.404
Margin of error = ± 0.404 * 1.96 = ± 0.079
Lower end = 0.413 – 0.079 = 0.334
Upper end = 0.413 + 0.079 = 0.492
We are 95% sure that the proportion of external managers is between 33.4% and 49.2%.