F-MBA SQA Final Exam
Problem 1 2 3 4 5 Total Points 10 10 10 20 10 60 Score

Exam Rules A. B. C. D. The exam is open-book and open-note. You can use only a calculator during the exam; but you cannot use a laptop. You are NOT allowed to discuss any issues with students in the class during the exam. Any kind of cheating during the exam will result in zero score with possibly further penalties by Korea University Business School.

I acknowledge and accept the above exam rules.

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Date:

FMBA SQA Final Exam

Prof. Kihoon Kim Oct. 10, 2012

1. Multiple and True/False Questions (10 points) Please circle the right answer for the questions below. Each question is assigned 2.5 points. 1. The sample mean of population 1 is smaller than that of population 2. If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, the a. null hypothesis should state µ1 − µ2 < 0 b. null hypothesis should state µ1 − µ2 ≤ 0 c. alternative hypothesis should state µ1 − µ2 < 0 d. alternative hypothesis should state µ1 − µ2 > 0 ANSWER: c

2.

A Type I error is committed when a. a true alternative hypothesis is not accepted b. a true null hypothesis is rejected c. the critical value is greater than the value of the test statistic d. sample data contradict the null hypothesis ANSWER: b In determining an interval estimate of a population mean when σ is unknown, we use a t distribution with a. n − 1 degrees of freedom

3.

b. c. d. ANSWER: 4.

n degrees of freedom
n − 1 degrees of freedom n degrees of freedom c

The purpose of statistical inference is to provide information about the a. sample based upon information contained in the population b. population based upon information contained in the sample c. population based upon information contained in the population d. mean of the sample based upon the mean of the...

...BUS 105e:
Statistics
By Dr Tony Halim
GBA: 27 February 2013
Done by:
Koh En Song Andrew (Q1211397)
Melissa Teo Kah Leng (E1011088)
Woon Wei Jie Jared
T 04
1.
Over the span of 100 days, the total revenue for Unicafe North and Unicafe West is $21876.60 and $22042.00 respectively. The average revenue for Unicafe North is $218.77. The average revenue for Unicafe West is $220.42. The highest revenue occurred on the 88th day for both outlets. The lowest revenue occurred on 39th day for both outlets. Generally, both outlets earn roughly the same amount of revenue each day.
2a.
Confidence interval is a range of values constructed from sample data so that the population parameter is likely to occur within that range at a specific probability (Lind, Marchal & Wathen, 2013).
Using the 95% level of confidence, the confidence interval for Unicafe West is 220.42 6.211. The confidence interval limits are $214.21 and $226.63 (rounded off to 2 decimal places).
Using the 95% level of confidence, the confidence interval for Unicafe North is 218.766 5.571. The confidence interval limits are $213.20 and $224.34 (rounded off to 2 decimal places).
In the event that Mr Yeung wants to predict his potential revenue for the next one hundred days, 95% of the confidence intervals would be expected to contain the population mean. The remaining 5% of the confidence intervals would not contain the population mean, average revenue earned per day....

...In today’s world, we are faced with situations everyday where Statistics can be applied. In general, Statistics is the science of collecting, organizing, and analyzing numerical data. The techniques involved in Statistics are important for the work of many professions, thus the proper preparation and theoretical background of Statistics is valuable for many successful career paths. Marketing campaigns, the realm of gambling, professional sports, the world of business and economics, the political domain, education, and forecasting future occurrences are all areas which fundamentally rely on the use of Statistics. Statistics is a broad subject that branches off into several categories. In particular, Inferential Statistics contains two central topics: estimation theory and hypothesis testing.
The goal of estimation theory is to arrive at an estimator of a parameter that can be implemented into one’s research. In order to achieve this estimator, statisticians must first determine a model that incorporates the process being studied. Once the model is determined, statisticians must find any limitations placed upon an estimator. These limitations can be found through the Cramer-Rao lower bound. Under smoothness conditions, the Cramer-Rao lower bound gives a formula for the lower bound on the variance of an unbiased estimator. Once the estimator is developed, it is tested...

...and Posttest with dependent (paired) samples
Hypothesis Testing in Regression-Null hypothesis: β=0/ t- statistic: t= b-b/sb
Average standard error test statistics DF
Sample to pop | | | | |
Sample mean with independent sample | | | | |
Pre and post test | | | | |
Interpretations:
Accept: the relationship/ answer is not statistically significant
Reject: the relationship/ answer is statistically significant.
Hypothesis testing is a statistical technique for evaluating whether a statement is more likely true or false.
EXAMPLE
Two hundred recipients are selected; 120 are randomly assigned to a workfare program, and 80 are assigned to a control group. By follow-up interviews, the state finds out how much income per week is earned by each individual, with the following results: Present a hypothesis and a null hypothesis, and evaluate them at the 1% and 0.1% level of type I error. State a conclusion in plain English. (30 points) mean for workfare 242.5 std 137. Control, mean 197.3 std 95.
Step 1: Formulate Hypothesis. Null is “no effect”
Ho workfare has no effect on wether an individual earns extra money
Ha workfare increases incentives for an individual to make extra money
Step 2: Calculate Sample statistics
Step 3: Decide Type I error
1% and .1%
Step 4: Calculate Test statistics
Step 5: Find P-value
if...

...sample observations are influenced by some non-random cause.
Hypothesis Tests
Statisticians follow a formal process to determine whether to reject a null hypothesis, based on sample data. This process, called hypothesis testing, consists of four steps.
State the hypotheses. This involves stating the null and alternative hypotheses. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false.
Formulate an analysis plan. The analysis plan describes how to use sample data to evaluate the null hypothesis. The evaluation often focuses around a single test statistic.
Analyze sample data. Find the value of the test statistic (mean score, proportion, t-score, z-score, etc.) described in the analysis plan.
Interpret results. Apply the decision rule described in the analysis plan. If the value of the test statistic is unlikely, based on the null hypothesis, reject the null hypothesis.
Decision Errors
Two types of errors can result from a hypothesis test.
Type I error. A Type I error occurs when the researcher rejects a null hypothesis when it is true. The probability of committing a Type I error is called the significance level. This probability is also called alpha, and is often denoted by α.
Type II error. A Type II error occurs when the researcher fails to reject a null hypothesis that is false. The probability of committing a Type II error is called Beta, and is often...

...that we are accepting the alternative hypothesis and this statement works vice versa. In this case that means that the null hypothesis can be rejected or disproving. For the data set that was given the null hypothesis also known as H-nought was µ1=µ2, while the alternative hypothesis is µ1<µ2. Null hypothesis states that the amount of rural nurse homes was equal to the average amount of beds used. Alternative hypothesis states that rural area nursing homes uses fewer amounts of beds. The claim indicated to what kind of test was going to be used and since I claimed that the rural area were going to have a lower average number of beds it states that the shaded area on the critical value test will be less than zero.
Table 1. Descriptive statistics for the given null and alternative hypothesis that includes the sample, mean, median, standard deviation, maximum values, and minimum values.
Sample Size
Mean
Median
Standard Deviation
Maximum Value
Minimum Value
Rural Area
34
0.6538
1.0000
0.4803845
1
0
Bed
4850
93.27
88.00
40.85273
244.00
25.00
Figure 1. This figure illustrates the critical value test for the left-tailed test. The critical value that was needed for the test was -1.692 according to the t-table since our sample size was 34. Used the degree of freedom formula to find the critical value.
Figure 2. This figure reflects to the p-value. When we figured out the p-value we used pt(t,33). Since pt(t,33) equaled 0.0137855 that indicated...

...of 1000 flights and proportions of three routes in the sample. He divides them into different sub-groups such as satisfaction, refreshments and departure time and then selects proportionally to highlight specific subgroup within the population. The reasons why Mr Kwok used this sampling method are that the cost per observation in the survey may be reduced and it also enables to increase the accuracy at a given cost.
TABLE 1: Data Summaries of Three Routes
Route 1
Route 2
Route 3
Normal(88.532,5.07943)
Normal(97.1033,5.04488)
Normal(107.15,5.15367)
Summary Statistics
Mean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary Statistics
Mean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131
Summary Statistics
Mean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From...

...of degrees of freedom of the test statistic? a. The number of degrees of freedom is 2. b. The number of degrees of freedom is 6. c. The number of degrees of freedom is 598. d. The number of degrees of freedom is 599. 3. A police oﬃcer believes that half of the cyclists ignore red traﬃc lights. To examine the issue, the police oﬃcer watches a busy crossroad with traﬃc lights from 8 AM till 10 AM. During these two hours 200 cyclists passed the crossroad. If indeed half of the cyclists ignore red traﬃc lights, what is the probability that at least 120 out of the 200 cyclists ignored the red traﬃc lights? a. That probability is approximately 0.000. b. That probability is approximately 0.002. c. That probability is approximately 0.998. d. That probability is approximately 1.000. 1
4. A researcher is interested in whether the location of population 1 diﬀers from that of population 2. She has gathered two independent samples. She has 3 observations from population 1: 12, 15, 9. Moreover, she has 4 observations from population 2: 10, 14, 13, 11. Using these samples, can the researcher conclude at a signiﬁcance level of 0.05 that the two population locations diﬀer? a. The relevant test statistic lies in the rejection region; the researcher can hence conclude that the two locations do not diﬀer. b. The relevant test statistic lies in the rejection region; the researcher can hence conclude that the two locations do diﬀer. c. The relevant...

...
November 19, 2010
NAME: The Statistics of Poverty and Inequality
TYPE: Sample
SIZE: 97 observations, 8 variables
DESCRIPTIVE ABSTRACT:
For 97 countries in the world, data are given for birth rates, death
rates, infant death rates, life expectancies for males and females, and
Gross National Product.
SOURCES:
Day, A. (ed.) (1992), _The Annual Register 1992_, 234, London:
Longmans.
_U.N.E.S.C.O. 1990 Demographic Year Book_ (1990), New York: United
Nations.
VARIABLE DESCRIPTIONS:
Columns
1 - 6 Live birth rate per 1,000 of population
7 - 14 Death rate per 1,000 of population
15 - 22 Infant deaths per 1,000 of population under 1 year old
23 - 30 Life expectancy at birth for males
31 - 38 Life expectancy at birth for females
39 - 46 Gross National Product per capita in U.S. dollars
47 - 52 Country Group
1 = Eastern Europe
2 = South America and Mexico
3 = Western Europe, North America, Japan, Australia, New Zealand
4 = Middle East
5 = Asia
6 = Africa
53 - 74 Country
Values are aligned and delimited by blanks.
Missing values are denoted with *.
The Statistics of Poverty and Inequality
This paper describes a case study based on data taken from the U.N.E.S.C.O. 1990 Demographic Year Book and The Annual Register 1992 giving birth rates, death rates, life expectancies, and Gross National Products for 97 countries.
When reviewing the statistics...