Assessment item 2—Assignment 2

Due date: 6:00pm, Friday, Week 10 ASSESSMENT

Weighting: 20% 2

Length: One file (.doc, .docx, .rtf or pdf) no more than 15 MB

Question 1 4 Marks

The following data shows the retail turnover (in $ millions) from January 2016 to September 2017 in Tasmania and Australian Capital Territory.

Month Turnover ; Tasmania ; Total ($ millions) Turnover ; Australian Capital Territory ; Total ($ millions)

Jan-2016 493.5 456.1

Feb-2016 495.3 458.8

Mar-2016 497.0 459.6

Apr-2016 498.4 459.5

May-2016 499.6 459.6

Jun-2016 500.8 460.8

Jul-2016 502.0 463.3

Aug-2016 503.6 466.4

Sep-2016 505.5 469.2

Oct-2016 507.0 471.2

Nov-2016 508.0 472.1

Dec-2016 508.4 472.4

Jan-2017 509.1 472.9

Feb-2017 510.5 474.2

Mar-2017 512.7 476.1

Apr-2017 515.2 477.8

May-2017 517.3 479.0

Jun-2017 518.6 479.3

Jul-2017 519.0 479.1

Aug-2017 518.9 478.6

Sep-2017 518.4 477.7

(a) Construct a stem-and-leaf display with one stem value in the middle, and Australian Capital Territory leaves on the right side and Tasmania leaves on the left side. (Must use EXCEL or similar for the plot.). 1 mark

(b) Construct a relative frequency histogram for Tasmania and a frequency polygon for Australian Capital Territory on the same graph with equal class widths, the first class being “$400 millions to less than $450 millions”. Use two different colours for Tasmania and Australian Capital Territory. Graph must be done in EXCEL) 1 mark

(c) Draw a group bar chart for both Tasmania and Australian Capital Territory and explain them. (Use 30 to 50 words to answer this part) 2 marks

Question 2 4 Marks

The following data shows the share prices (in dollars) of S&P/ASX 50 and S&P/ASX 200 in the month of October 2017.

Date S&P/ASX 50

Price ($) S&P/ASX 200

Price ($)

Oct 31, 2017 5,816.13 5,909.02

Oct 30, 2017 5,825.99 5,919.08

Oct 27, 2017 5,810.49 5,903.16

Oct 26, 2017 5,824.77 5,916.30

Oct 25, 2017 5,812.90 5,905.60

Oct 24, 2017 5,807.83 5,897.61

Oct 23, 2017 5,807.34 5,893.96

Oct 20, 2017 5,822.55 5,906.99

Oct 19, 2017 5,809.24 5,896.13

Oct 18, 2017 5,808.10 5,890.48

Oct 17, 2017 5,806.89 5,889.61

Oct 16, 2017 5,766.14 5,846.76

Oct 13, 2017 5,735.27 5,814.15

Oct 12, 2017 5,716.18 5,794.47

Oct 11, 2017 5,698.26 5,772.15

Oct 10, 2017 5,668.16 5,738.11

Oct 09, 2017 5,672.38 5,739.26

Oct 06, 2017 5,646.95 5,710.68

Oct 05, 2017 5,584.02 5,651.77

Oct 04, 2017 5,587.36 5,652.06

Oct 03, 2017 5,637.12 5,701.44

Oct 02, 2017 5,666.33 5,729.33

(a) Calculate the mean and standard deviation for S&P/ASX 50 and S&P/ASX 200

data. 1 mark

(b) Calculate the Minimum, Q1, Median, Q3 and Maximum values for S&P/ASX 50 and S&P/ASX 200 data. 1 mark

(c) Draw a box and whisker plot for the share prices for both S&P/ASX 50 and S&P/ASX 200 and put them side by side on one graph with the same scale so that the share prices can be compared. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.) 1 mark

(d) Discuss the overall performance of S&P/ASX 50 and S&P/ASX 200 in the month of October 2017. 1 mark

Question 3 4 Marks

The table below is taken from the Australian Bureau of Statistics website. It provides data on mortgage repayment (monthly) by Australian households living in different dwelling structures in the year 2011.

Dwelling Structure

Total occupied private dwellings Separate house Semi-detached, row or terrace house, townhouse Flat, unit or apartment

Mortgage Repayment (monthly)

Total 2 709 429 2 324 546 190 411 187 375

$0-$299 114 197 99 624 7 352 6 694

$300-$449 64 357 57 107 3 749 3 220

$450-$599 60 317 53 545 3 375 3 112

$600-$799 113 616 101 194 6 224 5 765

$800-$999 146 303 129 290 8 227 8 289

$1,000-$1,399 380 790 331 572 23 386 24 761

$1,400-$1,799 400 688 341 557 27 855 30 434

$1,800-$2,399 548 587 464 033 40 573 42 946

$2,400-$2,999 303 184 256 405 22 677 23 635

$3,000-$3,999 261 122 219 568 21 697 19 333

$4,000 and over 175 821 146 771 16 659 11 781

Mortgage repayment not stated 140 447 123 880 8 637 7 405

(a) Find the probability that a randomly selected households live in separate house dwelling? 1 mark

(b) In a total occupied private dwellings, what is the probability that a randomly selected households make a monthly mortgage repayment of $800-$999? 1 mark

(c) What is the probability that a randomly selected households make a monthly mortgage repayment of $1,800-$2,399 or $2,400-$2,999? 1 mark

(d) What is the probability that a randomly selected households make a monthly mortgage repayment of $300-$449 in a flat, unit or apartment dwelling structure? 1 mark

Question 4 4 Marks

(a) According to the 2017 Real Estate Statistics, residential property in Melbourne have increased by 13%. If a sample of 10 properties is taken, what is the probability of that exactly two or three residential properties have increased in their prices? 1 mark

(b) A customer service officer at a local bank serves an average of 10 customers per hour. What is the probability that the next customer will be served at least 5 minutes from now? 1 mark

(c) In a study conducted by a fast food restaurant, the average spending for a family of three is normally distributed with a mean of $27 and a standard deviation of $2.

(i) What proportion of the spending is between $25 and $35? 1 mark

(ii) What value do the upper 5% of the spending exceed? 1 mark

Question 5 4 Marks

(a) A travel agency acts as a selling agent for two airline companies. The two airline companies are charged the same monthly fee for this service and it is assumed that they will each receive approximately half the calls coming in. Based on this assumption, find the probability that in the next 150 calls 90 or more will be for one agent. (Use normal approximation of the binomial distribution.) 1 mark

(b) In 2017, it is found that 60% of video games purchasers are men. If a random sample is taken of 15 people who purchase video games, what is the approximate probability that there will be an exactly 11 men? 1.5 marks

(c) The personnel department of a large corporation employing 2,500 workers wants to find out whether men spend more than women in dental expenses. The study found that men spend a mean of $2,401 on dental expenses per year, whereas women spend a mean of $1,527 on dental expenses per year. Suppose that the study was based on a sample of 600 men and 700 females, and the standard deviation of the amount spent was $1,200 for men and $1,000 for women.

At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women? 1.5 marks

Due date: 6:00pm, Friday, Week 10 ASSESSMENT

Weighting: 20% 2

Length: One file (.doc, .docx, .rtf or pdf) no more than 15 MB

Question 1 4 Marks

The following data shows the retail turnover (in $ millions) from January 2016 to September 2017 in Tasmania and Australian Capital Territory.

Month Turnover ; Tasmania ; Total ($ millions) Turnover ; Australian Capital Territory ; Total ($ millions)

Jan-2016 493.5 456.1

Feb-2016 495.3 458.8

Mar-2016 497.0 459.6

Apr-2016 498.4 459.5

May-2016 499.6 459.6

Jun-2016 500.8 460.8

Jul-2016 502.0 463.3

Aug-2016 503.6 466.4

Sep-2016 505.5 469.2

Oct-2016 507.0 471.2

Nov-2016 508.0 472.1

Dec-2016 508.4 472.4

Jan-2017 509.1 472.9

Feb-2017 510.5 474.2

Mar-2017 512.7 476.1

Apr-2017 515.2 477.8

May-2017 517.3 479.0

Jun-2017 518.6 479.3

Jul-2017 519.0 479.1

Aug-2017 518.9 478.6

Sep-2017 518.4 477.7

(a) Construct a stem-and-leaf display with one stem value in the middle, and Australian Capital Territory leaves on the right side and Tasmania leaves on the left side. (Must use EXCEL or similar for the plot.). 1 mark

(b) Construct a relative frequency histogram for Tasmania and a frequency polygon for Australian Capital Territory on the same graph with equal class widths, the first class being “$400 millions to less than $450 millions”. Use two different colours for Tasmania and Australian Capital Territory. Graph must be done in EXCEL) 1 mark

(c) Draw a group bar chart for both Tasmania and Australian Capital Territory and explain them. (Use 30 to 50 words to answer this part) 2 marks

Question 2 4 Marks

The following data shows the share prices (in dollars) of S&P/ASX 50 and S&P/ASX 200 in the month of October 2017.

Date S&P/ASX 50

Price ($) S&P/ASX 200

Price ($)

Oct 31, 2017 5,816.13 5,909.02

Oct 30, 2017 5,825.99 5,919.08

Oct 27, 2017 5,810.49 5,903.16

Oct 26, 2017 5,824.77 5,916.30

Oct 25, 2017 5,812.90 5,905.60

Oct 24, 2017 5,807.83 5,897.61

Oct 23, 2017 5,807.34 5,893.96

Oct 20, 2017 5,822.55 5,906.99

Oct 19, 2017 5,809.24 5,896.13

Oct 18, 2017 5,808.10 5,890.48

Oct 17, 2017 5,806.89 5,889.61

Oct 16, 2017 5,766.14 5,846.76

Oct 13, 2017 5,735.27 5,814.15

Oct 12, 2017 5,716.18 5,794.47

Oct 11, 2017 5,698.26 5,772.15

Oct 10, 2017 5,668.16 5,738.11

Oct 09, 2017 5,672.38 5,739.26

Oct 06, 2017 5,646.95 5,710.68

Oct 05, 2017 5,584.02 5,651.77

Oct 04, 2017 5,587.36 5,652.06

Oct 03, 2017 5,637.12 5,701.44

Oct 02, 2017 5,666.33 5,729.33

(a) Calculate the mean and standard deviation for S&P/ASX 50 and S&P/ASX 200

data. 1 mark

(b) Calculate the Minimum, Q1, Median, Q3 and Maximum values for S&P/ASX 50 and S&P/ASX 200 data. 1 mark

(c) Draw a box and whisker plot for the share prices for both S&P/ASX 50 and S&P/ASX 200 and put them side by side on one graph with the same scale so that the share prices can be compared. (This graph must be done in EXCEL or similar software and cannot be hand-drawn.) 1 mark

(d) Discuss the overall performance of S&P/ASX 50 and S&P/ASX 200 in the month of October 2017. 1 mark

Question 3 4 Marks

The table below is taken from the Australian Bureau of Statistics website. It provides data on mortgage repayment (monthly) by Australian households living in different dwelling structures in the year 2011.

Dwelling Structure

Total occupied private dwellings Separate house Semi-detached, row or terrace house, townhouse Flat, unit or apartment

Mortgage Repayment (monthly)

Total 2 709 429 2 324 546 190 411 187 375

$0-$299 114 197 99 624 7 352 6 694

$300-$449 64 357 57 107 3 749 3 220

$450-$599 60 317 53 545 3 375 3 112

$600-$799 113 616 101 194 6 224 5 765

$800-$999 146 303 129 290 8 227 8 289

$1,000-$1,399 380 790 331 572 23 386 24 761

$1,400-$1,799 400 688 341 557 27 855 30 434

$1,800-$2,399 548 587 464 033 40 573 42 946

$2,400-$2,999 303 184 256 405 22 677 23 635

$3,000-$3,999 261 122 219 568 21 697 19 333

$4,000 and over 175 821 146 771 16 659 11 781

Mortgage repayment not stated 140 447 123 880 8 637 7 405

(a) Find the probability that a randomly selected households live in separate house dwelling? 1 mark

(b) In a total occupied private dwellings, what is the probability that a randomly selected households make a monthly mortgage repayment of $800-$999? 1 mark

(c) What is the probability that a randomly selected households make a monthly mortgage repayment of $1,800-$2,399 or $2,400-$2,999? 1 mark

(d) What is the probability that a randomly selected households make a monthly mortgage repayment of $300-$449 in a flat, unit or apartment dwelling structure? 1 mark

Question 4 4 Marks

(a) According to the 2017 Real Estate Statistics, residential property in Melbourne have increased by 13%. If a sample of 10 properties is taken, what is the probability of that exactly two or three residential properties have increased in their prices? 1 mark

(b) A customer service officer at a local bank serves an average of 10 customers per hour. What is the probability that the next customer will be served at least 5 minutes from now? 1 mark

(c) In a study conducted by a fast food restaurant, the average spending for a family of three is normally distributed with a mean of $27 and a standard deviation of $2.

(i) What proportion of the spending is between $25 and $35? 1 mark

(ii) What value do the upper 5% of the spending exceed? 1 mark

Question 5 4 Marks

(a) A travel agency acts as a selling agent for two airline companies. The two airline companies are charged the same monthly fee for this service and it is assumed that they will each receive approximately half the calls coming in. Based on this assumption, find the probability that in the next 150 calls 90 or more will be for one agent. (Use normal approximation of the binomial distribution.) 1 mark

(b) In 2017, it is found that 60% of video games purchasers are men. If a random sample is taken of 15 people who purchase video games, what is the approximate probability that there will be an exactly 11 men? 1.5 marks

(c) The personnel department of a large corporation employing 2,500 workers wants to find out whether men spend more than women in dental expenses. The study found that men spend a mean of $2,401 on dental expenses per year, whereas women spend a mean of $1,527 on dental expenses per year. Suppose that the study was based on a sample of 600 men and 700 females, and the standard deviation of the amount spent was $1,200 for men and $1,000 for women.

At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women? 1.5 marks

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