Q1 Consider the hourly payments of a random sample of employees of a food processing plant given in Dirhams below:
150, 200, 225, 160, 182, 185, 190, 177, 182, 195, 178, 140, 180, 190, 194, 155, 163, 202, 168, 170, 130, 210, 199, 174, 188, 193, 175, 165, 245, 220, 205, 180, 145, 179, 190, 215, 210, 235,245, 195.
a. Organize the data in ascending order
b. Find the median and the mode
c. Find the first and third quartiles
d. Calculate the mean and standard deviations of the sample.
e. Construct a bar chart using interval size of 10 dirhams
f. Find out if the distribution of hourly rates is left or right skewed.
g. How are the mean and median related in your distribution?
Q 2 Suppose that a population hasμ = 50 and σ= 10.
a) What is the Z value for x = 75?
b) What is the Z value for x = 40?
Q2 The next two questions refer to the following table where x= the number of days per week that 100 clients use a particular exercise facility.
|
X (# of days)
|
Frequency (# of people)
|
Cumulative Frequency
|
|
0
|
3
|
|
|
1
|
12
|
|
|
2
|
33
|
|
|
3
|
28
|
|
|
4
|
11
|
|
|
5
|
9
|
|
|
6
|
4
|
|
a. Complete the column of cumulative frequency
b. What is the 80th percentile?
c. Find the interquartile range.
d. Find the mean and standard deviation
Q 3 Suppose that the price of stock A is AED 25 and its standard deviation is 5. The average market price for all similar stocks is AED 20.Another stock B has a price of 30 and standard deviation of 15. Which stock performed better relative to the market?
Q 4 A black and red die are thrown and let X be a random variable denoting the sum of the dice.
a. Find all sample points of the experiment.
b. What is X's expected value, variance and the standard deviation?
c. What percent of the values of X lie within two standard deviations from the mean?
d. What is the probability of getting a sum of 7 in the experiment?
Q 5 Suppose that you observe the following service times (in minutes) by a bank teller: 1, 2, 1, 7, 2, 4.
a. What is the mean service time?
b. What is the variance and standard deviation?
c. What is the coefficient of variation?
Q 6 A researcher finds a claim in the newspapers that the average room rate (ARR) of all Abu Dhabi hotels is $163 per night. The researcher takes a sample of 25 hotels in Abu Dhabi and obtains a sample average room rate of $166. Assume that the standard deviation for Abu Dhabi hotels room rates, σ =10.
a. Test: H0 μ = 163, H1 μ ≠ 163, α = 0.05
b. Interpret your results.
c. Construct a 95% confidence interval for the mean and provide a description of the meaning of the confidence interval.
Q 7 A property manager thinks that the average rent for one-bed room flat his city has gone up to AED 6000 per month. He took a sample of 60 flats and found out that the sample mean was AED 6015 and sample standard deviation was 40.
a. Test the claim that the mean rent is 6000 or less (H0 μ ≤ 6000, H1 μ > 6000,
α = 0.05, assume
b. Interpret your test results in the context of the problem.
Q 8 A researcher wants to know how consumption spending responds to changes in disposable income. The researcher obtains 25 observations of consumption and disposable income from the national accounts of the country. After looking at a scatter plot of consumption and disposable income, the researcher finds the linear regression model to be appropriate and estimates the model: y = a + bx + e and obtains the following results;
y = 60+0.7x
se(b) = 0.3
se(a) = 15
adj-R2 = 0.90
a. Interpret the slope in the context of the problem.
b. Evaluate the overall fit of the model.
c. By how much would consumption increase if disposable income rises by 10 dirhams? What happens to the rest of the increase in disposable income?
d. Predict the level of consumption if disposable income is 80,000
e. Interpret the constant term.
Q 9 The table below contains average house prices, median income, average monthly rent and percentage of flats that are vacant in a given city.
|
House price
(HP)
|
Median Income (MI)
|
Rent
(R)
|
Vacant (V)
|
|
90
|
22
|
392
|
10
|
|
101
|
23
|
402
|
9
|
|
63
|
24
|
394
|
12
|
|
89
|
19
|
345
|
15
|
|
99
|
22
|
406
|
11
|
|
112
|
25
|
455
|
8
|
|
82
|
22
|
315
|
23
|
|
78
|
18
|
330
|
20
|
|
97
|
24
|
370
|
12
|
|
86
|
18
|
368
|
16
|
|
88
|
21
|
335
|
14
|
|
100
|
20
|
412
|
8
|
|
99
|
21
|
380
|
10
|
|
134
|
25
|
442
|
6
|
|
88
|
20
|
306
|
20
|
|
77
|
17
|
322
|
23
|
|
97
|
23
|
357
|
13
|
|
97
|
22
|
366
|
10
|
|
116
|
23
|
441
|
8
|
|
107
|
20
|
422
|
7
|
|
84
|
19
|
345
|
16
|
|
77
|
18
|
339
|
15
|
|
129
|
27
|
444
|
7
|
|
76
|
18
|
305
|
18
|
|
95
|
20
|
375
|
11
|
Answer the following questions using the data in the table
a. Run a linear regression of HP on MI, R and V and obtain a regression summary output.
b. What is the equation of the regression line?
c. Interpret the constant term and the slope coefficients in the context of the model
d. Evaluate the overall fit of the model using the adjusted R2
e. Find the error for predicting house price with median income, rent and vacant of 23, 441 and 8, respectively.
Q 10 Suppose that a financial analyst wants to evaluate the variability of the prices of a new stock in the market. The analyst collects closing stock prices of new stock issues: 15, 14, 19, 16, 11, 14, 10, and 9.
a. Compute the mean price of the stock
b. What is the median price?
c. Compute the variance and standard deviation
d. Describe the variability of the stock.