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MATH1030 Statistics for Business Assignment

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Added on: 2022-11-10 06:49:02
Order Code: 475210
Question Task Id: 0

Question 1 - 8 – Type The Letter Corresponding To Your Answers In Table Provided

1

 

2

 

3

 

4

 

5

 

6

 

7

 

8

 

 

 

Question 1 - 4 (1 mark each = 4 marks)

 

The number of students attending the weekly tutorial for the last 7 weeks was recorded as follows:

 

23, 23, 18, 26, 20, 31, 20

 

1. What is the sample mean?

A   23

B   22

C   25

D   24

2. What is the median?

A   26

B   23

C   22

D   4

3. What is the sample variance?

A   19.333

B   16.571

C   4.397

D   4.071

4. What is the sample range?

A   -3

B   8

C   13

D   20

 

Question 5 - 8 (1 mark each = 4 marks)

 

A survey was conducted to determine whether if a customer would recommend the store is independent to the store’s location. The result of the survey is tabulated for the following possible responses and the store’s location.

 

 

Sydney CBD

Parramatta CBD

Total

Would recommend

20

60

80

Would not recommend

10

10

20

Total

30

70

100

 

Let W be the event that the customer would recommend the store and

Let M be the event that the store’s location is Sydney CBD.

 

5. What is P (M)?

A   0.20

B   0.30

C   0.80

D   0.67

6. What is the P (M W)

?

A   0.20

B   0.60

C   0.90

D   0.30

7. What is the P (M U W)

?

A   0.10

B   0.60

C   0.90

D   0.30

8.

What is the P (M | W)?

A   0.20

B   0.67

C   0.90

D   0.25

 

 

 

Question 9 - 15 – Type The Letter Corresponding To Your Answers In Table Provided

 

9

 

10

 

11

 

12

 

13

 

14

 

15

 

 

 

 

Question 9 - 12 (1 mark each = 4 marks)

 

A fast food franchise is deciding between four locations for its new store. The locations and expected revenues are shown in the table along with the likelihoods that the store will be popular or unpopular.

 

Probability

Location A

Location B

Location C

Location D

Popular

0.7

50,000

40,000

25,000

30,000

UnPopular

0.3

20,000

40,000

65,000

40,000

9.      

What is the EMV for Location A?

A   70,000

B   35,000

C   50,000

D   41,000

10.     

Based on maximising EMV, what           location should be selected?

A   A

B   B

C   C

D   D

11.      What is the EPPI?

A  

115,000

B   54,500

C  70,000

D  23,500

12. A market research firm has offered to do a study that will guarantee the franchiser that they can select the best location. What is the most that the franchiser should be willing to pay for such a research report?

A   20,500

B  14,500

C  13,500

D  17,500

 

 

Question 13 - 15 (1 mark each = 3 marks)

 

A bank has a savings account in which it knows that the balance across all accounts is normally distributed, with a mean of $8000 and a standard deviation of $1000.

 

13.

The bank pays a higher rate of interest for accounts with a balance over $9500. Approximately, what proportion of accounts qualifies for this higher rate of interest?

A   0.9332

B   0.8413

C   0.0668

D  0.0062

              

14.The bank intends to write to account holders with balances in the bottom 3%. Approximately what will be the cut-off level (to the nearest dollar) below which an account holder will receive a letter?

A   6120

B  9880

C   7512

D  6200

 

15. If 16 accounts are selected at random, find the probability that the average balance is more than $ 8500?

A  0.0228

B   2

c   0.9772

D  0.7486

 

 

Questions 16 - 20 – Type Your Answers In Space Provided

 

Question 16 [4 marks]

 

A sample of 100 employees from a company had their annual sales recorded. The results gave a mean salary of $19,500. From past experiences, it is known that the standard deviation of mean salaries is $2,500. Construct a 95% confidence interval for the true average salary of all employees.

Question 17 (6 marks]

 

Researchers compared an experimental drug with the standard drug for the treatment of a certain disease, 300 were given the experimental drug and 500 were given the standard drug. The number of patients who recovered from each group were recorded as follows

 

 

Experimental Drug

Standard drug

Number of patients in Total

300

500

Number of recovered patients

225

371

 

Can we conclude, at the 10% level of significane, that the experimental drug had a higher proporion of recovered patients than the standard drug?

Question 18 (7 marks)

 

In consumer marketing, a common problem that any marketing manager faces is the selection of appropriate colours for package design. Assume that a marketing manager wishes to compare five different colours of package design. He is interested in knowing which of the five the most preferred one is so that it can be introduced in the market. A random sample of 400 consumers reveals the following:

 

Colour

Red

Blue

Green

Pink

Orange

Preference

70

106

80

70

74

 

Can we conclude, at five percent level of significance, that the consumer preference for package colours shows a significant difference?

Question 19 (2 + 2 = 4 marks)

 

The following random sample of 8 data values were obtained in a study of the relationship between the selling price of a three-bedroom unit (in thousands of dollars) and its assessed value (in thousands of dollars):

 

One-Bedroom Unit

1

2

3

4

5

6

7

8

Assessed Value ($1000’s) (x)

780

800

740

860

750

660

720

850

Selling Price ($1000’s) (y)

940

1020

890

1160

880

720

920

1140

 

You may use the following Excel print-outs or summary statistics provided to answer the questions

 

SUMMARY OUTPUT

 

 

SUMMARY STATISTICS

Regression Statistics

 

n =

8

Multiple R

0.973

 

?

=

770

R Square

0.947

 

? =

958.75

Adjusted R Square

0.939

 

s2x =

4485.714

Standard Error

35.918

 

s2y =

20983.93

Observations

8

 

sxy =

9442.857

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Intercept

-662.174

156.593

-4.229

0.006

Assessed Value

2.105

0.203

10.385

0.000

 

a)       Determine the linear regression equation to predict the selling price of a three-bedroom unit from its assessed value.

b)       Predict the approximate selling price of a comparable three-bedroom unit with an assessed     value of $800,000.

Question 20 (2 + 2 = 4 marks)

 

A role of the NSW Department of Social Services is to monitor the cost of goods and services in the state. Recent reports reveal that the price of commonly purchased supermarket items has doubled over the past ten years, and this is a concern for the department. In June 2015 the department investigated the findings of the report by regularly sending officials out to a typical supermarket in their area. The officials are asked to purchase a basket of food whose items that are commonly bought – these include eggs (by the dozen), milk (two litre bottle), bread (by the load), and potatoes (by the kilogram). The following information summarises the average yearly price of each item in the basket and the quantity typically bought (per year) for the years 2005 and 2015.

 

 

Quantity

Price

 

2005

2015

2005

2015

Eggs (dozen)

45

35

2.35

4.20

Milk (2L)

50

48

1.50

2.48

Bread (loaf)

50

50

0.92

1.98

Potatoes (kg)

48

50

4.21

7.26

 

a)       Calculate a simple aggregate price index for 2015, taking 2005 as the base year.

b)         Calculate the Paasche price index for 2015, taking 2005 as the base year.

 

 

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  • Posted on : November 10th, 2022
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