Statıstıcs Iı Final 8. Deneme Sınavı
Toplam 20 Soru1.Soru
In a binomial test, if the P is 0.40, what is the value of Q?
|
0.50 |
|
0.30 |
|
0.20 |
|
0.60 |
|
0.80 |
Q=1-P
Q=1-0.40
Q=0.60
2.Soru
The correlation coefficient between two variables is 0.45. What is the coefficeint of determination in this problem?
|
0.2025 |
|
0.3025 |
|
0.4025 |
|
0.6025 |
|
0.8025 |
C.D.= r^2= 0.45^2=0.2025
3.Soru
If the proportion of married people in a group is 0.63, what is the proportion of single people in the group?
|
0.17 |
|
0.27 |
|
0.37 |
|
0.50 |
|
0.63 |
If we know the proportion P for one class, the proportion of Q for the other class must be equal to 1 – P. Because the total probability must be equal to 1 and there are only two possible outcomes. For example, if the proportion of married people in a group is P = 0.63 then the proportion of the single in that group is Q=1-P = 1- 0.63 = 0.37. The correct answer is C.
4.Soru
In Hurwicz criterion, if the value of coefficient of optimism is equal to 1, what is the state of the mind of decision maker?
|
Pessimistic |
|
Realistic |
|
Doubtful |
|
Optimistic |
|
Cost effective |
In a paper in 1951, Leonard Hurwicz suggested a new method that balances the optimism and pessimism of the decision maker. In this method, the decision maker is allowed to have best and worst possible outcomes considered. In order to achieve this, Hurwicz suggests the use of coefficient of optimism. It is symbolized with ? and it is a decimal number between 0 and 1. If ? = 1, then the decision maker is hundred percent optimistic. If ? = 0, then the decision maker is hundred percent pessimistic. Since ? is the level of optimism we may easily call 1 – ? as the level of pessimism in the decision problem. Therefore, by changing the value of the ?, the decision maker may try to balance the optimism and pessimism.
5.Soru
If the correlation coefficient is 0.45, what is the value of coefficient of determination?
|
0.4545 |
|
0.1525 |
|
0.2535 |
|
0.2025 |
|
0.5025 |
(0.45)^2=0.2025
6.Soru
The payoff values for decision alternatives : there are 5 states of nature and the profit value for the first decision alternative is 15 according to optimist and 12 according to pessimist. If coefficient of optimism is 0.6, what is payoff value for the first decision alternative?
|
14.25 |
|
14.00 |
|
13.80 |
|
13.75 |
|
13.45 |
x = 15 . 0.6 + 12 (1 – 0.6) = 9 + 4.8 = 13.8 . pg. 194 . Correct answer is C.
7.Soru
Total price and quantity for products group A is 40 and 8, and 60 and 7, as unit a and unit b, for years X and Y, respectively. What is the Fisher’s price index for A for year Y when year X is the base ?
|
74 |
|
80 |
|
1400 / 3 |
|
1500 / 7 |
|
1600 / 21 |
Fisher's index = (Laspeyres' index . Paashe's index)1/2 ; for this case : Laspeyres' inden . Paashe's index = Fisher's index ; x = ((40 . 8) / (60 . 7)) . 100 = (320 / 420) . 100 = 1600 / 21
8.Soru
Which index is known as the average of weighted relative prices since it is a composite index number of prices formed by the weighted sum method?
|
Fisher’s Ideal Index |
|
Paasche's Index |
|
Laspeyres’ Index |
|
Consumer Price Index |
|
Chain-Based Simple Index |
Laspeyres Index was created by the German economist Étienne Laspeyres. The technique designed by Laspeyres uses base-period weights. It consists of the information about the price and quantity of products in different periods. The weighting scheme makes it a better tool than simple indexes. By using the Laspeyres index, it is possible to make a comparison of today’s price and quantity between the price and quantity of items altogether for a base period. The Laspeyres price index is also known as the average of weighted relative prices since it is a composite index number of prices formed by the weighted sum method. The index is found by the ratio of the sum of prices in the current period to the sum of the prices in the base period, these sums are weighted by the respective quantities of the base period. In this case, the weights which are used are the quantities of each commodity in the base period. So, it measures the relative price change of the commodities when the respective quantities are considered unchanged. The correct answer is B.
9.Soru
A decision alternative has 2 and 4 as payoff values and the probabilities of the associated states of nature are 0.25 and 0.75 respectively. What is the expected monetary value of this decision alternative?
|
2.25 |
|
2.75 |
|
3.25 |
|
3.50 |
|
3.75 |
x = 2 . 0.25 + 4 . 0.75 = 0.50 + 3 = 3.5 . pg. 197 . Correct answer is D.
10.Soru
the variable a has values 10, 12, 14, 18, 19 and the variable b has values 2, 6, 4, 9, 2. What is the value of Pearson's correlation coefficient?
|
0.267 |
|
0.125 |
|
0.987 |
|
0.36 |
|
0.08 |
Using the equation
the result is 0.267
11.Soru
According to data, when the Pearson's correlation coefficient is found as 0.974, how should the relationship between the variables be interpreted ?
|
Perfect correlation |
|
Very strong correlation |
|
Moderate correlation |
|
Weak correlation |
|
No correlatipn |
As the number gets closer to 1, the correlation is stronger. Therefore if it is 1, it is perfect correlation and if it is 0, there is no correlation. In this example, correlation is almost 1, therefore it shows a very strong correlation. The correct answer is B.
12.Soru
What is the expected monetary value of this profit based payoff matrix?
|
200.45 |
|
225.70 |
|
251.65 |
|
300.25 |
|
350.45 |
13.Soru
Total price and quantity for products group A is 15 and 8, and 25 and 6, as unit a and unit b, for years X and Y, respectively. What is the Paasche’s price index for A for year X when year Y is the base?
|
250 |
|
150 |
|
80 |
|
60 |
|
45 |
x = ((15 . 8) / (25 . 6)) . 100 = (120 / 150) . 100 = 80
14.Soru
In Wilcoxon Rank Sum Test n1=45 and n2=40 then what is the value of E[S]?
|
2000 |
|
1935 |
|
1800 |
|
1725 |
|
1635 |
E(S)=(45*(45+40+1))/2=1935
15.Soru
A decision alternative has 80 and 30 as payoff values and the probabilities of the associated states of nature are 0.60 and 0.40 respectively. What is the expected monetary value of this decision alternative?
|
63 |
|
60 |
|
57 |
|
50 |
|
43 |
x = 80 . 0.6 + 30 . 04 = 48 + 12 = 60 . pg. 197 . Correct answer is B.
16.Soru
What is the non-parametric alternative of t test?
|
ANOVA |
|
Chi-Square |
|
Mann-Whitney dependence |
|
Wilcoxon Rank Sum Test |
|
Binomial |
The parametric independent samples t test is based on several assumptions: two samples are independent of each other, the populations in the investigation for t test are normally distributed, and two populations that these two samples are taken from has the same variability. The Wilcoxon rank sum test is a non- parametric alternative test that involves less assumptions. Especially it does not require that our two populations have a specific known distribution. As long as the populations in question are independent and has the same variability, you may use Wilcoxon Rank Sum test. Therefore, if you want to know if two samples come from independent populations, this method is a good choice. Wilcoxon rank sum test assumes that the two population distributions are identical, although they may differ in location parameter, such as one distribution may be shifted to the right or to the left of the other distribution.
17.Soru
How is the power of a statistical test calculated?
|
α - 1 |
|
β - 1 |
|
β + α |
|
1– β |
|
1 - α |
An additional important concept in statistical hypothesis testing is the power of the statistical test. The power of a statistical test is defined as the probability of rejecting the null hypothesis (H0 ) when the alternative hypothesis is actually true. Therefore, it could be inferred as the probability of correctly rejecting a null hypothesis (H0 ) when it is actually false. Then the power of a statistical test can be calculated as 1– β.
18.Soru
The method of finding the degree of relationship between the variables is called ____________________?
The method of finding the degree of relationship between the variables is called ____________________?
|
t test |
|
z test |
|
Mann-Whitney U test |
|
ANOVA |
|
Correlation analysis |
The method of finding the degree of relationship between the variables is called correlation analysis.
19.Soru
Decision maker defines the coefficient of optimism as 0.34 , then what is the coefficient of pessimism?
|
0.17 |
|
0.34 |
|
0.66 |
|
0.68 |
|
0.83 |
x = 1 – 0.34 = 0.66 . pg. 194 . Correct answer is C.
20.Soru
what do we call "P(fail to reject the null hypothesis H0 when it is actually false)"?
|
Correct decision |
|
1-β |
|
β + α |
|
α |
|
β |
through a hypothesis-testing, it is also important to consider the probability of a type II error, failing to reject the null hypothesis (H0) when it is false, which is denoted by β. Then the type II error probability is,
β = P(type I error) = P(fail to reject the null hypothesis H0 when it is actually false)
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