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## Question :

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 2.8 3.6 3.75 3 2.5 2.7 3.5 3.9 2.95 3.3

 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