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DATA ANALYSIS AND DECISION MAKING MGMT5504

PRACTICE Quiz Paper

PART A: Multiple Choice questions (30 marks). This section contains 15 questions, each worth 2 marks. Please attempt to answer ALL questions.

A1 An employee engagement survey was conducted within a large organisation. This was done by randomly selecting 10 stores and surveying all employees within those stores. Which sampling method has been used?

a) Cluster sampling.

b) Judgement sampling.

c) Simple random sampling.

d) Stratified sampling.

e) Non-probability sampling. 

A2 Which one of the following statements about the mean is false?  

a) It is a measure of a “typical” value.

b) It is equal to the median in a “bell-shaped” normal distribution.

c) It is calculated by adding together all values then dividing by the total number of values.

d) It is equal to the mode in a “bell-shaped” normal distribution.

e) It is less affected by extreme values than the median.

A3 The manager of a chain of jazz clubs wanted to determine the demographics of patrons visiting the clubs. Three clubs were selected for study. Descriptive statistics relating to the age of patrons are presented below.  

Club	Mean Age (years)	Standard Deviation
A	29	12.3
B	58	6.4
C	43	3.7

Which one of the following statements is false?

a) The average age of patrons at Club C is 43 years.  

b) All patrons visiting club A are younger than all patrons visiting Club B and Club C.

c) The patrons visiting Club A are the youngest, on average, for the three clubs.

d) Club A has the largest variation in the age of patrons.  

e) In theory, 68% of the patrons visiting Club C would be aged between 39.3 and 46.7.

A4 The distribution below shows the time taken to complete a task (measured in minutes). The distribution is described as:   

 

a) Left (negatively) skewed.

b) Right (positively) skewed.

c) Normally distributed.  

d) Uniformally distributed.

e) There is not enough information provided.

A5 In Question A4 above, the graphical device used to present the data is a: a) pie chart

b) bar chart

c) histogram

d) ogive

e) polygon

Questions A6 and A7 relates to the following information.  

A researcher wanted to determine which factors contribute to an individual’s happiness. To do so the researcher randomly selected 100 individuals and collected data on the following variables:  1) happiness (measured on a scale of 1 to 5 where 5 = extremely happy, 4= somewhat happy, 3= neutral, 2= somewhat unhappy, 1 = extremely unhappy); 2) age (measured in years); 3) whether the individual is studying (measured as 0= not currently studying, 1= currently studying); 4) whether or not the individual is married (measured as 0=not married, 1=married); 5) hours worked (measured as the number of hours worked per week); and 6) golf (measured as the number of hours the individual played golf per week). The correlation matrix is presented below. 

Correlations 

	Happiness	Age	Studying	Married	Hours_Worked
Happiness	1	.725**	.462**	.490**	-.477**
Age	.725**	1	.262**	.353**	-.354**
Studying	.462**	.262**	1	.490**	-.304**
Married	.490**	.353**	.490**	1	-.339**
Hours_Worked	-.477**	-.354**	-.304**	-.339**	1
Golf	.531**	.407**	.405**	.299**	-.190

**. Correlation is significant at the 0.01 level (2-tailed).

A6 Which of the above variable(s) is/are nominal?

a) Happiness and Age.

b) Happiness, Age and Golf.

c) Studying and Married.

d) Happiness, Age, Golf and Hours_Worked.

e) Married.

A7 Referring to the correlation matrix, describe the relationship between ‘age’ and ‘happiness’.  

a) Strong, positive.

b) Weak, positive.

c) Strong, negative.

d) Weak, negative.

e) No relationship.

A8 A Masters student wanted to determine whether full-time Masters students spend, on average, more than 40 hours per week on their studies. Which test is appropriate to analyse the data?

a) One-sample t-test.

b) Independent-samples t-test.

c) Paired-samples t-test.

d) All of the above.  

e) None of the above.

A9 To test the research scenario in question A8 above, which pair of hypotheses are most appropriate?

a) H₀:  μ = 40 hours, H_A: μ ≠ 40 hours

b) H₀: μ ≤ 40 hours, H_A: μ > 40 hours

c) H₀: μ ≥ 40 hours, H_A: μ < 40 hours

d) H₀: μ ≠40 hours, H_A: μ =40 hours

e) H 40 hours, H_A: c> 40 hours.

A10 If the p-value was calculated at 0.070, using an alpha level of 5%, what would be the researcher’s decision?

a) Reject H₀ as the p-value is less than the alpha level.  

b) Reject H₀ as the p-value is greater than the alpha level.  

c) Do not reject H₀ as the p-value is less than the alpha level.  

d) Do not reject H₀ as the p-value is greater than the alpha level.  

e) None of the above.  

A11 Assume the population distribution for commuting times to work is right-skewed with a mean of 20 minutes. According to central limit theory, with a sample size of 500 the sampling distribution is likely to be:

a) Right-skewed with a mean of 20.

b) Left-skewed with a mean of 20.

c) Approximately normally distributed with a mean of 20.

d) Uniformly skewed with a mean of 20.

e) Not enough information is provided to answer this question.

A12 For the following normal distribution, what is the likely probability value for the shaded area?

a) 0.50.

b) 0.75.

c) 0.45.

d) 0.20.

e) 0.90.

A13 If the waiting time at a bank is normally distributed with a mean of 5 minutes and a standard deviation of 1 minute, according to the empirical rule which ONE of the following statements is true?

a) No customer will wait longer than 7 minutes.

b) 68% of customers wait between 2 and 3 minutes.

c) 95% of customers wait between 4 and 6 minutes.

d) 99.7% of customers wait between 2 and 8 minutes.

e) More than 50% of customers wait longer than 5 minutes.

 Question A14 relates to the correlation matrix below. This matrix shows the relationships between stress (1=low stress, 10=high stress), coffee consumption (cups per day), exercise (hours per week), hours worked (per week), and height (in centimetres). The researcher is interested in which factor(s) influence stress.  

	stress	coffee consumption	exercise	hours worked	height
stress	1
coffee consumption	0.850918	1
exercise	‐0.91144	‐0.715378701	1
hours worked	0.557329	0.530625261	‐0.4686	1
height	0.548448	0.395726613	‐0.49463	0.255060311	1

A14 Referring to the correlation matrix, which one of the following statements is correct?

a) The variables ‘stress’ and ‘hours worked’ are negatively correlated.  

b) There is a moderate, positive correlation between ‘height’ and ‘exercise’.  

c) There is a weak, negative correlation between ‘exercise’ and ‘coffee consumption’.

d) The correlation between ‘coffee consumption’ and ‘stress’ indicates that as ‘coffee consumption’ increases, stress decreases.

e) There is a moderate, negative correlation between ‘hours worked’ and ‘exercise’.

A15 Which one of the following statements about the standard deviation is not true?

a) It is used to measure the variability of a data set.

b) It is the square root of the variance.

c) It is measured as the difference between the mean and the data point nearest to the mean.

d) The symbol for the sample standard deviation is ‘s’.

e) It is measured in the same units as the units of the data.

PART B: The following section contains three case studies with short answer questions. (30 marks). Please attempt to answer ALL questions.

Case Study 1 (10 marks) 

Contains 5 questions. Please attempt to answer ALL questions.

The average wait time at the “Busy Bean” coffee shop is 3.5 mins. After putting on more staff, the manager wants to know if the wait time is now significantly less than 3.5 minutes. A survey of 15 customers revealed a mean wait time of 3.3 minutes and a standard deviation of 0.12 minutes. Assume an alpha level of 5%.

1. State the null hypothesis in words and statistical notation. (2 marks)

2. State the alternative hypothesis in words and statistical notation. (2 marks)

3. Calculate the appropriate (Z or t) test statistic. (3 marks)

4. Determine the critical value and make a decision (i.e. reject H₀ or do not reject H₀). (Show workings). (2 marks)

5. Draw a conclusion in response to the manager’s query. (1 mark).

Case Study 2 (10 marks)  

Contains 4 questions. Please attempt to answer ALL questions.

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes.

1. What is the probability that a call takes longer than 9.5 minutes? (2 marks)

2. What is the probability that a call takes between 5 minutes and 10 minutes. (2 marks)

3. For a random sample of 10 calls, what is the probability that the average call time is longer than 9.5 minutes? (3 marks)

4. The manager has decided to have a signal system attached to the phone so that after a certain period of time, a sound will occur on the employees' phone if an employee exceeds the time limit. The manager wants to set the time limit at a level so that it sounds for only 8% of all calls. What should the time limit be set? (3 marks)

Case Study 3 (10 marks)  

Contains 5 questions. Please attempt to answer ALL questions.

According to the Synergy website, “$298 is the average WA energy bill” for two months. However, there is also a disclaimer stating “Approximate only, based on the average consumption of a residential customer calculated using the current A1 tariff.” A market research company wanted to determine the accuracy of this claim. They conducted a survey to determine if the average energy bill was indeed $298. To do so, 201 households were randomly selected. The mean cost for their energy bills was $296 with a standard deviation of $40. Is the statement made by Synergy correct or does it need to be changed? Assume an alpha level of 5%.  

1. State the null hypothesis in words and statistical notation. (2 marks)

2. State the alternative hypothesis in words and statistical notation. (2 marks).

3. Calculate the appropriate (Z or t) test statistic. Show workings. (2 marks)

4. Identify the critical value and make a decision (i.e. reject H₀ or do not reject H₀). (Show workings). (2 marks)

5. Draw a conclusion in relation to the case study question. (2 marks)