Bus5Sbf Statistics For Business And Assessment Answers

Answer:

Task 1

A random sample of two hundred households has been collected in Excel. The sampling method used in this case is simple random sampling. Simple random sampling is the sampling method in which the sampling units are selected randomly with the probability of selecting each unit being the same.

This is the best method of selecting the sample as with the help of this method samples can be selected from a population with a minimum information about the population. Detailed information about the population is not required. Classification errors are not present in this type of sampling. Simple random sampling represents the whole population and is bias free. Analyzing data becomes easier with the sample collected using this technique (Fowler, 2013). This is a very simple technique and can be used easily. The sampling errors can also be assessed very easily using this method.

Part C

The standard deviation of the annual expenses of alcohol consumption in the households is 2093.185, for the consumption of meals the standard deviation is 1577.824, the standard deviation for annual expenditures on consumption of fuel is 1665.23 and for phone is 1755.425. Thus, the deviation is maximum in case of annual expense of alcohol consumption and minimum in case of annual expense of consumption of meals. It is an appropriate measure of variability because the standard deviation measures the distance of the values from the median. Thus, this measure can show how much the values of the distribution are close to the mean or away from the mean.

Part D

From the box and whisker plot in figure 1, it can be seen that, the annual expenditure on alcohol is most variable followed by phone, fuel and meals. It can also be seen that the minimum household expenditure on alcohol is zero. Thus, there are families who do not consume alcohol. From the descriptive statistics, it can be seen that the mean of all the four variables are greater than the median, which is again greater than the mode. Thus, the distributions of the expenses are negatively skewed. This means that more families spend high on the consumption of these four variables such as alcohol, meals, fuel and phone.

Task 2

Part B

• The percentage of households that spend on utilities at the most $ 1200 per annum is 68 percent.
• The percentage of households that spend on utilities between $1200 and $ 2400 per annum is (17.5 + 6.5 + 4) % = 28 percent.
• The percentage of households that spend on utilities more than $ 2400 is (1.5 + 1 + 1.5) = 4 percent.

Part C

The utility expenditures are not normally distributed. Moreover, the distribution of the annual income on utilities is positively skewed. Thus, it can be said that very less families spend more on utilities. The distribution is not normally distributed because the normal distribution is symmetric. From the histogram in figure 2.1, it is very clear that the distribution is not symmetric.

Task 3

The top 10 percent value of the household’s annual after tax income is the 90^th percentile and the bottom 10 percent value of the household’s annual after tax income is the 10^th percentile. For this data, the top 10 percent value of annual after tax income is $122673.5 and the bottom 10 percent value of the household’s annual after tax income is $19842. From this, it can be said that 10 percent of the population of households have an annual after tax income of $122,673 and above. 10 percent of the household have an annual after tax income below $19,842.

The mean of the variable OwnHouse is found to be 0.67. The variable OwnHouse contains two values 0 and 1. Here, 0 implies that the household does not own a house and 1 indicates that the household owns a house. The mean is found to be greater than 0.5. Thus it can be said that most of the households own a house.

In the sample of 200 households, the number of households having a family size of 5 is 17. Thus, the probability that a randomly selected household will have a family size equal to 5 is given by (17/200) = 0.085.

From the scatter diagram in figure 3.1, it can be seen clearly that the correlation between the two variables such as the natural logarithm of total expenditure and natural log of annual after tax income is very less (0.117). Nothing can be predicted about one variable from the value of the other variable.

Task 4

From the table, it can be seen that the number of males undergoing higher level of education is (21 + 15) = 36 and the number of women undergoing higher level of education is (12+26) = 38. These two values are more or less equal and thus can be said that male and female heads of the households do not differ in their higher level of qualification. In this case higher level of qualification has been considered as bachelor’s degree and master’s degree.

Part B

The probability that the head of the household is a female and her higher level of education is intermediate is (26/200) = 0.13.

Part C

The probability that the head of the family is a male and has bachelor’s degree is (21/200) = 0.105.

Part D

The proportion of having secondary as the highest degree from among females is ((23+23)/200) = 0.23.

Part E

The two events “gender of household head is male” and “having the master’s degree” will be independent if the probability of intersection of the two events is equal to the product of the probabilities of the two events separately. The probability of gender of a household head being male is (90/200) = 0.45. The probability of having a master’s degree is (41/200) = 0.205. The probability of a household head being male and having a master’s degree is (15/200) = 0.075. Now, (0.45*0.205) = 0.092 which is not equal to 0.075. Thus, the two events are dependent.  

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2014). Statistics for business & economics, revised. Cengage Learning.

Carlberg, C. (2014). Statistical analysis: microsoft excel 2013. Que Publishing.

De Finetti, B. (2017). Theory of probability: A critical introductory treatment(Vol. 6). John Wiley & Sons.

Fowler Jr, F. J. (2013). Survey research methods. Sage publications.

Miller, I., & Miller, M. (2015). John E. Freund's mathematical statistics with applications. Pearson.

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2015). Introduction to linear regression analysis. John Wiley & Sons.

Rodgers, K. A. (2016). Correlation Analysis with Excel Handout.

Triola, M. F. (2013). Elementary statistics using Excel. Pearson.