Business Statistics

 

Business Statistics

 

 

Introduction

Business statistics has emerged to be one of the most sought areas of study. This is because the concepts involved in business statistics are very important in opening the mind for use when it comes to decision making. Business statistics is known to hold important lessons regarding the process of decision making in the event of uncertainties (Upton & Cook, 2001). It imparts knowledge touching on identifying a population for study, doing sampling successfully, calculating measures such as the mean, median and mode among others.

Question 1

The samples obtained are:

(665-3111, 888- 8210, 303- 3566), (783- 4616, 658- 5286, 404-9473), (253-7846, 349-9949, 409-2393),( 143-8596, 303-0303, 303-9765), (860-7358, 564-8696, 415-4970), (742-3586, 965-4697, 876-5372), (889-2543,658-9607,856-5465),(686-2376,977-5328,909-8964),(268-5074,326-4859,742-8500),(753-9894,559-7523,287-0753),(425-5860,662-3427,508-7962),(315-3869,985-3749,094-4098), (434-5564, 545-5746, 356-5464), (535-6487, 454-6575, 675-5464), (546-5465, 657-6475, 658-6435), (678-5435, 554-5364, 874-5532), (545-6478, 665-6474, 776-6543), (776-6575, 665-4578, 864-5474)(536-7977, 675-6474, 675-6654) and (536-5464, 854-9836, 634-7468)

The 4th, 5th and sixth digits for each of the phone numbers are as follows

(311,  821,   356), (461, 528, 947), (784, 994, 239),( 859, 030, 976), (735, 869, 497), (358, 469, 537), (254,960,546),(237,532,896),(507,859,850),(989,752,753),(586,342,796),(386,374,409), (556, 574, 546), (648, 657, 546), (546, 647, 643), (543, 536, 553), (647, 647, 654), (657,457, 547)(797, 647, 665) and (546, 983, 746)

Question 1 (a)

Mean of the 20 samples is given as below.
Total for each sample Mean
1488 496
1936 645.33
2017 672.33
1865 621.67
2101 700.33
1364 454.67
1,760 586.67
1,665 555.00
2,216 738.67
2,494 831.33
1,724 574.67
1,169 389.67
1676 558.67
1851 617.00
1836 612.00
1632 544.00
1948 649.33
1069 356.33
2109 703.00
2275 758.33

 

Therefore, the mean of the samples is given by the total of the sample means divided by the number of samples.

Therefore the means of the 20 samples=12,065/20=603.25

Question 1 (b)

Histogram showing the 20 samples
Question 1 (c)

The distribution involved in the analyzed data is regular. This is evidenced by the fact the diagram represents recurring ups and downs at regular intervals. The sample items are not widely dispersed.

Question 1 (d)
20 more samples

Total per sample Mean
964 321.33
1565 521.67
1472 490.67
2008 669.33
2165 721.67
1948 649.33
1933 644.33
1565 521.67
1231 410.33
1557 519.00
1381 460.33
1855 618.33
1375 458.33
2061 687.00
1853 617.67
1778 592.67
1876 625.33
1708 569.33
1805 601.67
1177 392.33

After adding two more samples, the diagram is as follows

There shows normal distribution since all the values are falling within the three categories as per the empirical statistical rule.
Question 2 (a)
The formula for a z-score is

z = (x – μ) / σ

The z-score formula factors in:
z = z-score
x = raw score or observation to be standardized
μ = mean of the population
σ = standard deviation
z = (46.5 – 43) / 5.2
z-score = 3.5/5.2=0.67

Question 2 (b)
The z-score can be used to calculate probabilities. This is because the z-score is able to tell determine the extend values defy the mean.

Question 3 (a)
Null Hypothesis:  The single family homes sales for this year are higher than those of last year.

Alternative hypothesis: The single family homes sales for this year are not higher than those of last year.
Question 3 (b)

Null Hypothesis: The low-fat cheesecake is not as good as that of traditional cheesecake.

Alternative Hypothesis: The low-fat cheesecake is as good as that of traditional cheesecake.
Question 3 (c)

Null Hypothesis: music lessons have a positive effect on a child’s self-esteem

Alternative Hypothesis: Music lessons have a neutral effect on child’s self-esteem
Question 3 (d)

Null Hypothesis: More males than females drive truck-type vehicles

Alternative Hypothesis: Equal males and females drive truck-type vehicles

Conclusion

Statistics is one of the tools which are quite useful in data analysis. It is important for everyone to understand the basics so as to be able to handle statistical problems with ease. Things such as population, mean, medium, mode, sampling and presentation of data analysis are some of the important things to get knowledge about. Additionally, learning how to carry out hypothesis testing is also important. This is made better by getting conversant with how to come up with the null and alternative hypothesis.

References

Upton, G. & Cook, I. (2001). Introducing Statistics. Oxford University Press.

 

 

 

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