HI6007 Statistics For Business Decisions Assignment

Question 1(10 marks - 2 marks per question)

1. In your own words, define and give example of each of the following statistical terms.
   1. Population
   2. Sample
   3. Parameter
   4. Statistic
2. For each of the following examples of data, determine the data type.

• The age of children attending childcare in Pallara Suburb in Queensland
• The nationality of foreign students studying at Holmes Institute
• How likely are you to recommend our services to your friends? Very likely, Likely, Neutral, Unlikely, Very unlikely
• The number of High Distinction grade received by students in a statistics unit
• List any two methods of conducting a survey of respondents. Also give an important advantage and disadvantage of each of the methods listed.
• How do point estimators and interval estimators differ?
• The mean and median score in a Chemistry exam is 68 and 64, respectively. Due to the high level of difficulty of the exam, the lecturer decides to give 6 bonus points to every student. What will be the new mean and median scores? Provide a brief explanation.

Question 2(10 marks - 2 marks per question)

The height of five children (two-digit values in centimeters) in a childcare centre of Sunny bank suburb are recorded as follows.

17 25 20 25 38

1. Calculate the mean and median of the sample data
2. What is the mode and the range of the sample data?
3. Calculate the variance and the standard deviation of the sample data
4. Calculate the coefficient of variation
5. Calculate the 40th percentile

Question 3(10 marks)

A random sample of 500 households in the Brisbane suburb showed that 300 of them owned at least one car. Establish a 90% confidence interval for the true proportion of households in this suburb who own a car by using the following template to answer this question.

1. What is the parameter of interest? (0.5 mark)
2. What is the point estimator? (0.5 mark)
3. What is the associated sampling distribution (how do you know this?). (1 mark)
4. Specify the formula for the 90% confidence interval estimator for the parameter. (1 mark)
5. Perform the necessary calculations and write down the lower and upper limits of the 90% confidence interval. (5 marks)
6. Interpret the calculated confidence interval. (2 marks)

Question 4(10 marks)

A researcher wants to analyse the relationship between beer price (in $/per litre) and per-capita beer quantity consumed (in litres) in Australia between 1978-2020. To analyse the relationship between beer price and per capita beer quantity consumed, the researcher carried out a regression analysis and the excel output is given below.

Required:

Using the Regression summary output table, answer the following:

1. Comment on the strength and the direction of the relationship between beer price and per-capita quantity of beer consumed rates.(1 mark)
2. Write down the estimated regression line.(1 mark)
3. What do the estimated regression coefficients reveal about the relationship between per-capita beer quantity consumed and price of beer? (3 marks)
4. Comment on the fitness of the estimated model. (2 marks)
5. Test whether a linear relationship exists between beer price and per capita beer quantity consumed at the 5% significance level using the following template. (3 marks)
   (Use the Excel output)
   Step 1. Statement of the hypotheses
   Step 2. Test statistic and the standardized test statistic
   Step 3. Level of significance
   Step 4. Decision rule
   Step 5. Computation of the value of the test statistic:
   Step 6. Conclusion

Question 5(10 marks)

The starting salary of Bachelor of Business graduates in Australia is known to be normally distributed. An Australian university claims that the average starting salary of its graduates has increased since 2017. The average salary in 2017 was $60,000. A sample of 36 graduates were chosen from the batch of 2021. The average salary and the standard deviation in the sample was found to be $62,000 and $4,800 respectively. A prospective student wishes to investigate the University’s claim at 1% level of significance.

Required:

Use the following 6 step procedure to arrive at your conclusion.

Step 1. Statement of the hypotheses (2 marks)

Step 2. Test statistic and the standardized test statistic (0.5 mark)

Step 3. Level of significance (0.5 mark)

Step 4. Decision rule (2 marks)

Step 5. Computation of the value of the test statistic (2 marks)

Step 6. Conclusion (3 marks)

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