ECON 2331: Economic and Business Statistics 2
Assignment 2 (75 marks; 5%)
To receive full marks, you need to show all your work.
1. Social networking is becoming more and more popular around the world.
Pew Research Center used a survey of adults in several countries to
determine the percentage of adults who use social networking sites (USA
Today, February 8, 2012). Assume that the results for surveys in Great Britain, Israel, Russia, and United States are as follows: (31 marks total)
|
|
Country
|
|
Great
Britain
|
Israel
|
Russia
|
United
States
|
|
Use Social
Networking Sites
|
Yes
|
344
|
265
|
301
|
500
|
|
No
|
456
|
235
|
399
|
500
|
a. State the null and alternative hypotheses. (2 marks)
b. Conduct a test to determine whether the proportion of adults using social networking sites is equal for all four countries. What is the degrees of freedom? (10 marks)
c. What is the p-value? (2 marks)
d. Using a 5% level of significance, what is your conclusion? (2 marks)
e. What are the sample proportions for each of the four countries? (2 marks)
f. Which country has the largest proportion of adults using social networking sites? (2 marks)
g. Using a 5% level of significance, conduct multiple comparison tests
among the four countries. What is your conclusion? What is the degrees of freedom?(11 marks)
2. Based on sales over a six-month period, the five top-selling compact cars are Chevy Cruze, Ford Focus, Hyundai Elantra, Honda Civic, and Toyota Corolla (Motor Trend, November 2, 2011). A sample of compact car sales in Chicago showed the following number of vehicles sold: (17 marks total)
|
Cars
|
Vehicles Sold
|
|
Chevy Cruze
|
108
|
|
Ford Focus
|
92
|
|
Hyundai Elantra
|
64
|
|
Honda Civic
|
84
|
|
Toyota Corolla
|
52
|
a. State your null and alternative hypotheses. (2 marks)
b. Use a goodness of fit test to determine if the sample data indicate that the market shares for the five compact cars in Chicago are different than the market shares reported by Motor Trend. Show all the steps in your calculations of this test, including the degrees of freedom. (9 marks)
c. Using a 5% level of significance, what is the p-value for this test? (2 marks)
d. What is your conclusion? (2 marks)
e. What market share differences from others, if any, exist in Chicago? (2 marks)
3. We want to determine if the following sample comes from a normal distribution: (15 marks total)
|
105
|
260
|
314
|
400
|
520
|
280
|
270
|
516
|
419
|
520
|
|
300
|
306
|
115
|
200
|
208
|
420
|
438
|
511
|
708
|
300
|
|
418
|
110
|
410
|
312
|
360
|
420
|
519
|
702
|
690
|
518
|
|
310
|
314
|
418
|
316
|
412
|
510
|
700
|
650
|
670
|
612
|
|
516
|
480
|
490
|
504
|
518
|
460
|
600
|
680
|
692
|
600
|
a. Compute the mean and the standard deviation. (3 marks)
b. Compute the test statistic. Hint: divide the distribution into 10 equal intervals. (8 marks)
c. At 95% confidence using the critical value approach, test to determine if the sample comes from a normal population. (2 marks)
d. Compute the p-value. (2 marks)
4. Prior to the start of the season, it was expected that audience proportions for the four major news networks would be CBS 28%, NBC 35%, ABC 22% and CBC 15%. A recent sample of homes yielded the following viewing-audience data:
|
|
Number of
Homes
|
|
CBS
|
850
|
|
NBC
|
980
|
|
ABC
|
670
|
|
CBC
|
500
|
We want to determine whether or not the recent sample supports the expectations of the number of homes of the viewing audience of the four networks. (12 marks total)
a. Clearly state the null and alternative hypotheses to be tested. (2 marks)
b. Compute the test statistic. Show all the steps in your calculations of this test including the degrees of freedom. (6 marks)
c. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. (2 marks)
d. What do you conclude? (2 marks)