Question 1 The following are marks, out of 100 obtained by 50 students in Quantitative Techniques class.

70 53 33 42 50 39 65 55 30 18
55 63 60 65 52 63 45 52 35 46
47 51 39 61 33 59 49 41 15 55
42 65 82 58 45 56 54 42 48 40
57 45 55 64 45 25 64 75 26 20
a) Make a frequency distribution taking a class interval of 10 marks.
b) Calculate: (i) Mean (ii) Median (iii) Mode and (iv) standard deviation of the ages
c) Compute the coefficient of variations and interpret the results

Question 2
In a study, physicians were asked what the odds of breast cancer would be in a woman who was initially thought to have a 1% risk of cancer but who ended up with a positive mammogram result (a mammogram accurately classifies about 80% of cancerous tumors and 90% of benign tumors.) 95 out of a hundred physicians estimated the probability of cancer to be about 75%. Do you agree?
Question 3
A student Tossed a coin twice in a class experiment. Let X = number of heads
(i) Construct a table to generate probabilities for X
(ii) Compute the expected values of X
(iii) Calculate the Variance and Standard deviations for X
(iv) ]Determine the covariance and interpret the results

Question 4
Assuming the mean and standard deviation of a normal distribution of 2,500 students test scores are 100 and 10 respectively, determine the number of students who
i. Scored 125
ii. Scored greater than 75?
iii. Scored less than 70?
iv. Scored between 80 and 110
v. Scored of at least 120?

Question 5
In an aptitude test the average grade was 65 and the standard deviation was 6. If 16% of the class are given A’s and the grades are curved to follow a normal distribution. What is the lowest possible A and the highest possible B?

Question 6
A study revealed that the average salary of a Quality Manager is less than Ghs 20,000 per annum. A sample of 45 Quality Managers have an average salary of Ghs 42,000. At α = 0.01, test the claim that, Quality Managers earn less than Ghs 20,000 per annum. The standard deviation of the population is Ghs 6000.

Question 7
A small publishing company decides to use one section of its plant to produce two textbooks called Microeconomics and Macroeconomics. The profit made on each copy is Ghs12 for Microeconomics and Ghs 18 for Macroeconomics. Each copy of Microeconomics requires 12 minutes for printing and 18 minutes for binding. The corresponding figures for Macroeconomics are 15 and 9 minutes respectively. There are 10 hours available for printing and 10.5 hours available for binding. How many of each should be produced to maximize profit?

Question 8
A study was conducted to determine whether Size, Location, City and Availability of water influences the price a house. For a sample of 5000 respondents been used in the study, an estimated house price model is presented in the tables below.

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.925022
R Square 0.855665
Adjusted R Square 0.711331
Standard Error 33.71296
Observations 9

ANOVA
df SS MS F Significance F
Regression 4 26951.75 6737.937 5.928342 0.04484
Residual 4 4546.254 1136.563
Total 8 31498

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 261.5252 85.7497 3.049867 0.038033 23.44586 499.6045 23.44586 499.6045
Size 0.119595 0.028634 4.176633 0.013956 0.040093 0.199097 0.040093 0.199097
Location -0.03518 0.025218 -1.39488 0.235521 -0.10519 0.03484 -0.10519 0.03484
City -0.05258 0.190096 -0.27662 0.795779 -0.58038 0.475209 -0.58038 0.475209
Availability of Water -0.05414 0.023918 -2.26371 0.046325 -0.12055 0.012263 -0.12055 0.012263

i. Write down the estimated model. (5 marks)
ii. Which of the variable(s) are statistically significant? (3 marks)
iii. Which of the variable(s) are statistically insignificant? (2 mark)
iv. What is the contribution of the four factors to the changes in house price?
(3 marks)
v. Interpret the R and R-Square values (3 marks)
vi. Is the overall model statistically significant? Prove. (4 marks)