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# PACC6008 Business Decision Making For Statistics And Graphical Representation

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• Course Code: PACC6008
• University: Newcastle University
• Country: United Kingdom

## Questions:

Question 1

Suppose Economics Web Institute conducted a research on US workers’ wage in 2018. They sent out a survey to a random sample of 536 workers and collected various information of them, including wage, occupation, sector, union, education, work experience, age, sex, marital status and living location. The data is reported in the Wage.xlsx data file.

(1) What is population Economics Web Institute is interested in?
(2) Use Microsoft Excel to conduct and present the appropriate graphic and descriptive analysis on two variables: wage and education, interpret the results, and prepare a report.

(3) Suppose Economics Web Institute also conducted the same survey in 2017, the proportion of workers with tertiary education was 0.45. They would like to know if this proportion has increased.

What is the appropriate statistics used here to test it?
What are the null and alternative hypotheses for this test?
Produce the test results using Microsoft Excel, interpret it and make a final conclusion.

(4) Suppose Economics Web Institute also conducted the same survey in 2017, the average wage per hour was \$30/hour. They would like to know if the average wage in 2018 is different from that in 2017.
What is the appropriate statistics used here to test it?
What are the null and alternative hypotheses for this test?
Produce the test results using Microsoft Excel, interpret it and make a final conclusion.

Question 2

Suppose you want to buy a three-bedroom property in Sydney and you are interested two main suburbs (Suburb 1 and Suburb 2) but you don’t know which one has higher average price. So you determined to do a research and see whether there is a significant difference of market price in these two suburbs. You are required to:

(1) Randomly select a sample of 40 properties in Suburb 1and another 40 properties in Suburb 2 and record their market prices. Thus, a total of 80 observations are recorded in your dataset. (Please see the data format attached the last page)

(2) What are populations you are interested in?

(3) Conduct your analysis using HYPOTHESIS TESTING AND ESTIMATION method.

Note: Check the conditions for the test identified.

(4) What conclusion you can make from the results for your decision making?

## Answer:

### Question 1

The institute is interested in wages of US workers in 2018.

Descriptive statistics and graphical representation of the variable Wages and Education is highlighted below (Foster, 2013).

Numerical summary

Graphical representation

Comment

### Wage Level

It is evident from the above computation that the mean hourly wage level is \$25.62. Also, the shape of the graph would be asymmetric considering that high positive skew is present which is also validated in the histogram. This implies that there is presence of outliers on the positive side. This can potentially distort the mean and hence central tendency may be better captured by the median hourly wage which is \$ 23.75. Also, the probability distribution related to the hourly wage would not be normal since skew is present and also the various central tendency measures differ in their magnitude (Rodgers, 2007). For a normal distribution, it is essential that these must coincide. The range of the hourly wage level varies from \$ 10 which is the minimum wage of about \$ 70. This is reflective of the great disparity in wages based on the underlying skill, experience and market dynamics. Also, the standard deviation about the mean is \$7.86 which implies moderate variation in the data (Stine & Foster, 2013).

### Education Level

The mean education level is 2.73 which indicates bachelor level represented by the number 3. The median level is 2 which imply that 50% of the sample individuals have only secondary degree. Further, skew is present in the data owing to few individuals falling in 5 bracket while 50% being restricted to secondary and primary level (Foster, 2013). The probability distribution would not be normal owing to the asymmetric shape of the graph as highlighted in the histogram obtained for the data provided. Besides, the deviation is data is captured from 1 to 5 where 1 highlights the lowest level i.e. primary education while 5 highlights the highest level i.e. PHD.

• Claim: Proportion of workers with tertiary education (Education = 3,4 &5) was 0.45.

The aim is to check the validity of the above shown claim with the help of hypothesis testing.

• Hypothesis testing for proportion would be taken into account to check the claim.
• The relevant null and alternative hypotheses are highlighted below (Rodgers, 2007):

### Null hypothesis

Alternative hypothesis

• Excel output for the hypothesis testing is shown below (Stine & Foster, 2013)
• Assuming level of significance = 5%
• Decision rule: Null hypothesis would be rejected when the p value is lower than the level of significance.
• It this case, it can be said that p value is higher than level of significance and therefore, insufficient evidence is present to reject the null hypothesis (Stine & Foster, 2017). Hence, alternative hypothesis would not be accepted and final, conclusion can be made that proportion of workers with tertiary education is lower than or equal to 0.45.
• Claim: Average wage per hour was \$30 per hour.

The aim is to check the validity of the above shown claim with the help of hypothesis testing.

• Hypothesis testing for one sample for mean would be taken into account to check the claim.
• The relevant null and alternative hypotheses are highlighted below:

### Alternative hypothesis

• Excel output for the hypothesis testing is shown below:
• Assuming level of significance = 5%
• Decision rule: Null hypothesis would be rejected when the p value is lower than the level of significance (Robert, 2010).
• It this case, it can be said that p value is lower than level of significance and therefore, sufficient evidence is present to reject the null hypothesis and to accept the alternative hypothesis. Hence, the conclusion can be drawn that average wage rate in 2018 is different from the 2017 wage level of \$30 per hour.

Question 2

• Prices (\$) of three bedroom property in New town and Hurstville suburb of Sydney have been taken into consideration and is highlighted below:

2) The populations that we are interested in comprises of all the houses located in New Town and Hurstville suburb which have three bedrooms. From these two populations defined above, the sample highlighted above has been selected.

3) The objective of this task is to infer based on the sample prices of houses in the two suburbs if the prices tend to differ in a significant manner or not. This would be carried out using hypothesis testing as the enabling tool.

The requisite hypotheses are highlighted below (Stine & Foster, 2017):

Null Hypothesis: µNewTown = µHurstville i.e. the average three bedroom house prices do not differ in a statistically significant manner from each other

Alternative Hypothesis: µNewTown ≠ µHurstville i.e. the average three bedroom house prices do differ in a statistically significant manner from each other

The relevant test statistics would be t considering that the population standard deviation is not known. Also, considering the alternative hypothesis, it would be correct to infer that the test would be two tailed. Hence, a two independent sample t test needs to be performed using MS-Excel. The relevant output is indicated below (Robert, 2010).

The two tail p value has come out as 0.00. Assuming a level of significance of 5%, it is apparent that the p value is lower than the assumed significance level. Thus, it may be concluded that the given evidence is sufficient to reject the null hypothesis and accept the alternative hypothesis.

4) The conclusion that can be drawn is that there is significant difference in the average price of three bedroom houses in the two selected suburbs. Therefore, a given individual based on the budgetary constraints can look for house in the suitable suburb.

## References

Foster, D. (2013) Statistics for Business: Decision Making and Analysis. (2nd ed.). London: Pearson Education Limited.

Robert, S.E. (2010) Statistics for Business: Decision Making And Analysis. Oxford: Oxford University.

Rodgers, P. (2007) Commercial Awareness and Business Decision Making Skill: How to understand and analyse company financial information. (4th ed.). New York: Butterworth-Heinemann.

Stine, R. & Foster, D. (2013) Statistics for Business: Decision Making and Analysis. (2nd ed.). London: Pearson College Division.

Stine, R. & Foster, D.P. (2017) Statistics for Business: Decision Making and Analysis. (3rd ed.).  London: Pearson.

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