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Bb108 Business Statistics For The Assessment Answers

Provide a statistical investigation of a business problem using mathematical or statistical methods.

Answer:

For company A

On the basis of the above, it is apparent that the distribution of crew is not normal as the measures of central tendency are not equal. Also, the extent of variation in crew numbers seem large as apparent from the measures of dispersion. The distribution of rooms cleaned is also non-normal. Also, the deviation tends to be high as for the crew distribution.

For company B

On the basis of the above, it is apparent that the distribution of crew is not normal as the measures of central tendency are not equal. Also, the extent of variation in crew numbers seem large as apparent from the measures of dispersion. The distribution of rooms cleaned is also non-normal. Also, the deviation tends to be high as for the crew distribution. 

It is apparent that the shape is not symmetric and also the corresponding distribution is non-normal. Also, there is presence of slight rightwards or positive skew. 

It is apparent that the shape is not symmetric and also the corresponding distribution is non-normal. Also, there is presence of slight rightwards or positive skew.

Based on the comparison of the two histograms, it is evident that the rooms cleaned are higher for company B in comparison to company A. This is especially apparent from the taller bars observed for the histogram corresponding to company B. 

It is apparent that company B seems to have a  more efficient crew in comparison with company A as for each of the 7 crew levels, the number of rooms cleaned is higher for company B in comparison with company A. However, this conclusion is being derived on the given sample data and inferential statistics technique needs to be applied so as to derive suitable conclusion for the population data based on the given sample data. 

New variable for each company would be determined with the help of formula shown below:

Ratio

For company A, this ratio would be termed as OCA

For company B, this ratio would be termed as OCB

Claim – Company B might have the higher mean value

Hypothesis testing:

Null hypothesis  

Alternative hypothesis

As per Central Limit Theorem, z test would be taken into consideration when the sample size is higher than 30. It is apparent that sample size is higher than 30 and hence it may seem that  z statistics can be used. However, it can be seen that standard deviation of population is unknown and therefore, z statistics cannot be used. Hence, it is fair to use t test in order to check the validity of the claim.

t – test with unequal variances would be computed in excel sheet and is highlighted below:

Level of significance (Alpha) = 5%

Critical value test would be used in the present case. Value of t critical for one tail test is 1.66 and the t stat is 3.64.  It is apparent that t stat value is much higher than critical value of t and therefore, sufficient evidence is present to reject the null hypothesis. Therefore, it can be concluded that company B does have high mean as compared with company A. Since, a higher mean is desirable as it indicates higher efficiency, thus it would be recommended to the client to choose company B over company A.

Company selected based on hypothesis testing is Company B.            

X = Number of crews

Y =Number of rooms cleaned

Linear Regression Model for the given data has been performed in excel sheet and the final output is furnished below:

Based on the above regression analysis, it is apparent that the explanatory variable is the number of crews while the dependent variable is the number of rooms cleaned. This clearly makes sense as the amount of rooms cleaned would essentially depend on the number of crews that are available. Larger would be the availability of crew and it would be expected that larger would be rooms cleaned.

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