Student Number: (enter on the line below)

Student Name: (enter on the line below)

HI6007 MID TERM

STATISTICS FOR BUSINESS DECISIONS

FINAL ASSESSMENT

TRIMESTER 2, 2022

TIME ALLOWED: 24 hours

Assessment Weight: 50 total marks

Instructions:

• All questions must be answered by using the answer boxes provided in this paper.

• Completed answers must be submitted to Blackboard by the published due date and time.

Please ensure you follow the submission instructions at the end of this paper.

Purpose:

This assessment consists of five (5) questions and is designed to assess your level of knowledge of the key topics covered in this unit.

Question 1 (10 marks)

a. Using your own words, differentiate descriptive statistics from inferential statistics.

(2 marks)

ANSWER a): ** Answer box will enlarge as you type

b. The sales per day, in dollars, at a retail store are given below.

1520 2620 3360 1350 2545

1430 2400 1550 2390 1560

i. Calculate the mean, median, first quartile and third quartile. (2 marks)

ANSWER b {i}:

ii. Calculate the variance and standard deviation, interquartile range and coefficient of variation. (2 marks)

ANSWER b {ii}:

iii. What conclusion can you reach about daily sales at this store. (4 marks)

ANSWER b {iii}:

Question 2 (10 marks)

The unit coordinator of the MBA statistics unit at Holmes institute wants to determine whether there are significant differences between student performance across campuses. A random sample of 18 students were selected with 6 students in each campus. The table below shows the student grades in T1 2022.

Campus Location

Melbourne Sydney Brisbane

75 55 77

68 70 55

79 65 70

90 60 60

65 70 65

72 78 70

At the 5% level of significance, is there evidence of a significant difference in students’ performance between three campuses? Use the six steps process of hypothesis testing to answer the question.

ANSWER:

Question 3 (10 marks)

a. Critically review the importance of residual analysis in regression (2 marks)

ANSWER a):

b. A researcher wants to assess the impact of interet rate and exchange rate on S&P/ASX 200 Benchmark Index. So, he gathered a data set from 1992 -2021. The below is the summarizes regression output. However, it is incompete to a certain extend.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.748527

R Square 0.560293

Adjusted R Square A

Standard Error 1159.889

Observations 30

ANOVA

df SS MS F Significance F

Regression 2 46285802 23142901 D 0.0000152

Residual B 36324234 C

Total 29 82610035

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 6394.028643 572.7939949 11.16288 0.0000000 5218.752444 7569.304841

Inflation Rates E 20261.7341 1.38328 0.1779114 -13545.99714 69601.29154

Interest Rates -63459.36165 10886.28913 -5.82929 0.0000033 -85796.18191 -41122.5414

Based on the above incomplete regression output, you are required to:

i. State the multiple regression equation. (1 mark)

ANSWER b {i}:

ii. Interpret the meaning of regression coefficients. (3 marks)

ANSWER b {ii}:

iii. Calculate the adjusted R square and interpret its meaning. (2 marks)

ANSWER b {iii}:

iv. Determine whether there is a significant relationship between dependent variable and the two independent variables at the 5% level of Significance. (2 marks)

ANSWER b {iv}:

Question 4 (10 marks)

Apex company is one of the main producers of Nutrition bars in Australia. The Production manager of Apex company has reported that the weight of each Nutrition bar is a normally distributed random variable with a mean of 31.7g and a standard deviation of 0.3g.

a. Find the probability that if a customer buys one chocolate bar, that bar will weigh less than 31.4g. (2.5 marks)

ANSWER a):

b. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be less than 31.4g. (2.5 marks)

ANSWER b):

c. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be greater than 31.4g. (2.5 marks)

ANSWER c):

d. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be between 31.4g and 31.9g. (2.5 marks)

ANSWER d):

Question 5 (10 marks)

a. Amiba Private limited produce 10 products in their production plant. The company’s research and development (R& D) department wants to estimate a price for their 11th product. Hence, R & D department has selected 10 sites thought to have essentially identical sales potential and offered the product in each location at a different price. The resulting sales are recorded in the following table.

You are required to find the equation of the regression line and forecast the sales if company fix the price at $15.25. (5 marks)

Location 1 2 3 4 5 6 7 8 9 10

Price 15.00 15.50 16.00 16.5 17.00 17.50 18.00 18.50 19.00 19.50

Sales ($’000) 15 14 16 9 12 10 8 9 6 5

ANSWER a):

b. Victorian government has proposed a new bus network to south east regional Victoria. A survey is sent out to residents asking questions which relate to:

1. The resident’s age

2. Frequency of bus use

3. Usual ticket type purchased

4. Main purpose of using the bus

i. Describe the population (1 mark)

ANSWER b {i}:

ii. Indicate whether each of the questions above is categorical or numerical.

(2 marks)

ANSWER b {ii}:

iii. Identify the possible scale of measurements on answers related to each of the questions. (2 marks)

ANSWER b {iii}:

iv. Develop two more numerical questions and state whether the variables are discrete or continuous. (3 marks)

ANSWER b {iv}:

END OF FINAL ASSESSMENT

Submission instructions

Before you submit your assessment, please check all of the following:

• You have named your file with your Student Number and Unit Code e.g. NTR1234 HI6007

It is critical you follow this file name instruction to ensure the file belongs to you.

• You have saved your file in MICROSOFT WORD format only. No other format is accepted.

• You have checked you are submitting the correct document as special consideration is not granted if you make a mistake.

Once you have checked the above:

Upload your file to the appropriate link on Blackboard.

You have two attempts to submit your assessment with only the final submission being marked.

** Note: All submissions are automatically passed through SafeAssign to assess academic integrity.

Student Name: (enter on the line below)

HI6007 MID TERM

STATISTICS FOR BUSINESS DECISIONS

FINAL ASSESSMENT

TRIMESTER 2, 2022

TIME ALLOWED: 24 hours

Assessment Weight: 50 total marks

Instructions:

• All questions must be answered by using the answer boxes provided in this paper.

• Completed answers must be submitted to Blackboard by the published due date and time.

Please ensure you follow the submission instructions at the end of this paper.

Purpose:

This assessment consists of five (5) questions and is designed to assess your level of knowledge of the key topics covered in this unit.

Question 1 (10 marks)

a. Using your own words, differentiate descriptive statistics from inferential statistics.

(2 marks)

ANSWER a): ** Answer box will enlarge as you type

b. The sales per day, in dollars, at a retail store are given below.

1520 2620 3360 1350 2545

1430 2400 1550 2390 1560

i. Calculate the mean, median, first quartile and third quartile. (2 marks)

ANSWER b {i}:

ii. Calculate the variance and standard deviation, interquartile range and coefficient of variation. (2 marks)

ANSWER b {ii}:

iii. What conclusion can you reach about daily sales at this store. (4 marks)

ANSWER b {iii}:

Question 2 (10 marks)

The unit coordinator of the MBA statistics unit at Holmes institute wants to determine whether there are significant differences between student performance across campuses. A random sample of 18 students were selected with 6 students in each campus. The table below shows the student grades in T1 2022.

Campus Location

Melbourne Sydney Brisbane

75 55 77

68 70 55

79 65 70

90 60 60

65 70 65

72 78 70

At the 5% level of significance, is there evidence of a significant difference in students’ performance between three campuses? Use the six steps process of hypothesis testing to answer the question.

ANSWER:

Question 3 (10 marks)

a. Critically review the importance of residual analysis in regression (2 marks)

ANSWER a):

b. A researcher wants to assess the impact of interet rate and exchange rate on S&P/ASX 200 Benchmark Index. So, he gathered a data set from 1992 -2021. The below is the summarizes regression output. However, it is incompete to a certain extend.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.748527

R Square 0.560293

Adjusted R Square A

Standard Error 1159.889

Observations 30

ANOVA

df SS MS F Significance F

Regression 2 46285802 23142901 D 0.0000152

Residual B 36324234 C

Total 29 82610035

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 6394.028643 572.7939949 11.16288 0.0000000 5218.752444 7569.304841

Inflation Rates E 20261.7341 1.38328 0.1779114 -13545.99714 69601.29154

Interest Rates -63459.36165 10886.28913 -5.82929 0.0000033 -85796.18191 -41122.5414

Based on the above incomplete regression output, you are required to:

i. State the multiple regression equation. (1 mark)

ANSWER b {i}:

ii. Interpret the meaning of regression coefficients. (3 marks)

ANSWER b {ii}:

iii. Calculate the adjusted R square and interpret its meaning. (2 marks)

ANSWER b {iii}:

iv. Determine whether there is a significant relationship between dependent variable and the two independent variables at the 5% level of Significance. (2 marks)

ANSWER b {iv}:

Question 4 (10 marks)

Apex company is one of the main producers of Nutrition bars in Australia. The Production manager of Apex company has reported that the weight of each Nutrition bar is a normally distributed random variable with a mean of 31.7g and a standard deviation of 0.3g.

a. Find the probability that if a customer buys one chocolate bar, that bar will weigh less than 31.4g. (2.5 marks)

ANSWER a):

b. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be less than 31.4g. (2.5 marks)

ANSWER b):

c. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be greater than 31.4g. (2.5 marks)

ANSWER c):

d. Find the probability that, if a customer buys a pack of four bars, the mean weight of the four bars will be between 31.4g and 31.9g. (2.5 marks)

ANSWER d):

Question 5 (10 marks)

a. Amiba Private limited produce 10 products in their production plant. The company’s research and development (R& D) department wants to estimate a price for their 11th product. Hence, R & D department has selected 10 sites thought to have essentially identical sales potential and offered the product in each location at a different price. The resulting sales are recorded in the following table.

You are required to find the equation of the regression line and forecast the sales if company fix the price at $15.25. (5 marks)

Location 1 2 3 4 5 6 7 8 9 10

Price 15.00 15.50 16.00 16.5 17.00 17.50 18.00 18.50 19.00 19.50

Sales ($’000) 15 14 16 9 12 10 8 9 6 5

ANSWER a):

b. Victorian government has proposed a new bus network to south east regional Victoria. A survey is sent out to residents asking questions which relate to:

1. The resident’s age

2. Frequency of bus use

3. Usual ticket type purchased

4. Main purpose of using the bus

i. Describe the population (1 mark)

ANSWER b {i}:

ii. Indicate whether each of the questions above is categorical or numerical.

(2 marks)

ANSWER b {ii}:

iii. Identify the possible scale of measurements on answers related to each of the questions. (2 marks)

ANSWER b {iii}:

iv. Develop two more numerical questions and state whether the variables are discrete or continuous. (3 marks)

ANSWER b {iv}:

END OF FINAL ASSESSMENT

Submission instructions

Before you submit your assessment, please check all of the following:

• You have named your file with your Student Number and Unit Code e.g. NTR1234 HI6007

It is critical you follow this file name instruction to ensure the file belongs to you.

• You have saved your file in MICROSOFT WORD format only. No other format is accepted.

• You have checked you are submitting the correct document as special consideration is not granted if you make a mistake.

Once you have checked the above:

Upload your file to the appropriate link on Blackboard.

You have two attempts to submit your assessment with only the final submission being marked.

** Note: All submissions are automatically passed through SafeAssign to assess academic integrity.

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