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STA101 Statistics for Business Assessment Answer

Assessment 1 - Assignment

Unit: STA101 – Statistics for Business


Total Marks:This assignment is worth 40 marks (40 % of the total marks in the unit).

Instructions:

Students are required to cover all stated requirements.

Your answer must be both uploaded to Moodle in word file and handed over a printed copy.

You need to support your answers with appropriate Harvard style references where necessary.

Include a title/cover page containing the subject title and code .

Each of the following question worth 10 marks, please answer all of them. If needed please use Harvard referencing style. There is no word limit, but it is necessary that you provide answers with explanations.

Question 1: (10 marks)

Given the following sample data:

x
420
610
625
500
400
450
550
650
480
565
y
2.80
3.60
3.75
3.00
2.50
2.70
3.50
3.90
2.95
3.30


1. Calculate the covariance and the correlation coefficient


2. Comment on the relationship between x and y


3. Determine the least squares line. 


4. Draw the scatter diagram and plot the least squares line. 

Question 2: (10 marks)

Consider the following Excel regression of perceived sound quality as a function of price for 27 stereo speakers. 

a. Is the coefficient of Price significantly different from zero at α = .05?

b. What does the R2 tell you? 

c. Given these results, would you conclude that a higher price implies higher sound quality? 

Regression 
Statistics

R Square
0.01104
Standard Error
4.02545
Observations
        27


Statistic
Coefficients
Std Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
88.4902
1.67814
52.731
0.0000
85.0340
91.9464
Price
−0.00239
0.00453
−0.528
0.6019
−0.01172
0.00693

Question3: (10 marks)

After researching cysts of a particular type, a doctor learns that out of 10,000 such cysts examined, 1,500 are malignant and 8,500 are benign. A diagnostic test is available which is accurate 80% of the time (whether the cyst is malignant or not). The doctor has discovered the same type of cyst in a patient.

  1. In the absence of any test, what is the probability that the cyst is malignant? What is the probability that the cyst is benign?
  2. What is the probability that the patient will test positive?
  3. What is the probability that the patient will test negative?
  4. What is the probability that the patient has a benign tumor if he or she tests positive?
  5. What is the probability that the patient has a malignant cyst if he or she tests negative?

Question4(10 marks)

Below are monthly rents paid by 30 students who live off campus:

  1. Find the mean, median, and mode. 
  2. Do the measures of central tendency agree? Explain. 
  3. Calculate the standard deviation. 
  4. Are there outliers or unusual data values? 
  5.  Using the Empirical Rule, do you think the data could be from a normal population?
730
 730
730
930
700
570
690
1,030
740
620
720
670
560
 740
650
660
850
930
600
 620
760
690
710
500
730
 800
820
840
720
700


Answer

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