Lost-time injury causes and percentage of occurrence

1. Cause is a nominal variable since it presents a series of labels which cannot be arranged in any logical order. If on the other hand, the labels could have been independently expresses in a logical sequence, then the variable would have been ordinal but this is not the case here.
2. The appropriate graph is bar chart.
3. Bar chart to represent the data

1. d) From the above chart, it is apparent that the most common cause of lost-time injury at the mining site has been through hit by a falling object. Other likely cause of lost-time injuries include same level fall or slip and also being cut by tools. Together, these three causes contribute to about 60% of the lost-time injuries incurred at the mining site. The other causes have relatively low incidence and thus, these major causes must be contained (Lehman & Romano, 2016).

Question 2

• Graphical display of distribution

Mean = 300 grams

Standard deviation =10 grams

• Company has the requirement of packets of balls of weight at least 280 grams.
• Graph

(ii) The understanding of the empirical rule can be highlighted using the following diagram.

In this case, since µ = 300g and σ = 10g, hence the rejected region would have a probability of 0.025.

1. c) 290 g is indicative of µ- σ while 330g is indicative of µ+ 3σ

The % of data lying between µ- 3σ and µ+3σ in accordance with the empirical rule is 99.7%. However, in order to obtain the answer for the given part, suitable deductions need to be made for the area between µ- σ and µ- 3σ (Lehman & Romano, 2016).

% values lying between µ- 3σ and µ- σ = 13.5% + 2.5% -[(100-99.7)/2]% = 15.85%

Hence, required probability = 0.997-0.1585 = 0.8385

Question 3

• Graphical display of survey score
• It is apparent from the above graph that the tail on the left side is longer than the one on the right which is indicative of the presence of negative skew (Shi & Tao, 2015). Since one of the key requirements of normal distribution is that the symmetric alignment of the normal curve, clearly the given distribution is not normal.
• Summary statistics

As negative skew is present along with potential outlier values speciality on the lower end, hence mean might be distorted to indicate a lower value. Thus, central tendency for the given data would be best represented using median which is not impacted by extreme values on either sides. Further, in relation to deviation, standard deviation may not be reliable and hence IQR or Inter-Quartile Range may be preferred (Shi & Tao, 2015).

• (i) Hypothesis testing   :

(ii)  The value of sample mean from the above shown descriptive statistics comes out to be 59.62. Hence, it can be said that values of sample mean and the hypothesized mean are similar.

(iii)  The value of t stat

(iv) The p value would be calculated as =1-T.DIST(3.90,299,TRUE) which comes out to be 0.0001.

(v) It can be seen that p value is lower than level of significance (0.02<0.05) and therefore, null hypothesis would be rejected and alternative hypothesis would be accepted  (Medhi, 2015).

(vi)  It can be concluded that the average satisfaction survey score of clients is not 55.

Question 4

• (i) Graphical display

(ii) The key difference as apparent from the above graph is that a higher satisfaction score is witnessed for larger clients in comparison to smaller clients. A key similarity is that majority of the satisfaction survey scores for both big and small clients are concentrated in the middle values with limited concentration in the extremes (Lind, Marchal & Wathen, 2016).

(b) Level of significance = 5%

(i) Hypothesis testing (Harmon, 2015)   :

(ii) The two tailed p value comes out to be 0.02.

(iii) It can be seen that p value is lower than level of significance (0.02<0.05) and therefore, null hypothesis would be rejected and alternative hypothesis would be accepted (Lehman & Romano, 2016).

(iv) It may be concluded that the satisfaction level across the big clients and small clients tends to differ which may be indicative of potential differential in providing service to these two groups.

(v) Management needs to link the incentive of project managers with the satisfaction level of clients irrespective of their underlying size. This would ensure that proper attention and customer service would be extended to both big and small clients.

Question 5

Pivot table

1. Probability that a person would travel in summer while selecting Coastal location.

Favourable case = 30

Total cases =80

Probability

1. Probability that a person would travel in winter while selecting Inland location (Medhi, 2015).

Favourable case = 20

Total cases =80

Probability

1. .Yes, there does seem to be an association since coastal location is preferred more in summer season as compared to winters. With regards to inland location, there does not seem to any preference of season.

1. Level of significance = 5%

• Hypothesis testing

Null hypothesis  Variables season and preferences are independent. 

Alternative hypothesis  Variables season and preferences are dependent. 

Chi – square test (Koch, 2016) 

• The p value comes out to be 0.0209.
• It can be seen that p value is lower than level of significance and therefore, null hypothesis would be rejected and alternative hypothesis would be accepted (Lind, Marchal & Wathen, 2016).
• Conclusion can be drawn that the underlying season does influence the preferred location of people to visit.

(e)  During winters, it is apparent that people tend to visit both inland and coastal locations and hence both need to be advertised. This is not the case in summers when coastal locations have a clear edge.

References

Harmon, M. (2015) Hypothesis Testing in Excel – The Excel Statistical Master (7^th ed.). Florida: Mark Harmon.

Koch, K.R. (2016) Parameter Estimation and Hypothesis Testing in Linear Models (2^nd ed.). London: Springer Science & Business Media.

Lehman, L. E. & Romano, P. J. (2016) Testing Statistical Hypotheses (3^rd ed.). Berlin : Springer Science & Business Media.

Lind, A.D., Marchal, G.W. & Wathen, A.S. (2016) Statistical Techniques in Business and Economics (15^th ed.). New York : McGraw-Hill/Irwin.

Medhi, J. (2015) Statistical Methods: An Introductory Text (4^th ed.). Sydney: New Age International.

Shi, Z. N. & Tao, J. (2015) Statistical Hypothesis Testing: Theory and Methods (6^th ed.). London: World Scientific.