Statıstıcs Iı Ara 7. Deneme Sınavı
Toplam 20 Soru1.Soru
The independent random sample sizes are n1 = 180 students and n2 =200 students. Also, the sample mean grades are 80 and 90. Population standard deviations are 20 and 40 respectively. What is the z value for the hypothesis testing?
The independent random sample sizes are n1 = 180 students and n2 =200 students. Also, the sample mean grades are 80 and 90. Population standard deviations are 20 and 40 respectively. What is the z value for the hypothesis testing?
|
-3.45 |
|
-4.59 |
|
-7.6 |
|
-0.89 |
|
-1.82 |
(80-90) / sqrt( 20^2/180 + 40^2/200) =-1.82
2.Soru
In a two population proportion problem x1 =50; n1=200; x2=120; n2 =400 then what is the value of joint p value?
|
0.08 |
|
0.12 |
|
0.15 |
|
0.25 |
|
0.28 |
(50 + 120) / (200 + 400) =0.28
3.Soru
The process of estimating a population parameter by a single number derived from the sample is called _______________ estimation?
The process of estimating a population parameter by a single number derived from the sample is called _______________ estimation?
|
Default |
|
Unknown |
|
Interval |
|
Variable |
|
Point |
The process of estimating a population parameter by a single number derived from the sample is called point estimation.
4.Soru
There are 28 red apples, 24 green apples, 16 immature apples, 32 red tomatoes, 16 green tomatoes, and 20 immatue tomatoes in a box. What is the population proportion estimate of immature things in this box ?
|
5 / 32 |
|
9 / 34 |
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11 / 90 |
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13 / 80 |
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15 / 128 |
x = (16 + 20) / (28 + 24 + 16 + 32 + 16 + 20) = 36 / 136 = 9 / 34. pg. 25 . Correct answer is B
5.Soru
In a two population hypothesis testing problem, the alternate hypothesis sign is not equal and the level of significance 0.05, what is the theoretical value of z from standard normal distribution?
|
1.88 |
|
1.96 |
|
2.58 |
|
2.33 |
|
2.87 |
From the standard normal distribution given in the page 79 of your book, the answer is 1.96.
6.Soru
What is a value that defines the characteristic of a whole population called?
|
Parameter |
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Mean |
|
Variance |
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Mode |
|
Median |
A parameter is a value that defines the characteristic of a whole population which means that population parameter consists of mean, variance, standard deviation, mode, median or proportion of the population or objects under consideration.
7.Soru
Interval estimation : the limits of the confidence interval are (4.1, 5.9), the significance level is 0.05. What is the sample arithmetic mean?
|
4.15 |
|
4.60 |
|
5.00 |
|
5.30 |
|
5.85 |
x = (4.1 + 5.9) / 2 = 5. pg. 33. Correct answer is C.
8.Soru
For a statistical test following a normal distribution, the alternative hypothesis is that the mean equals to a thousand and the standard deviation is ? = 24. A sample of 576 observations is randomly selected and the sample average is equal to 1020. What is the test statistic equal to?
|
5 |
|
10 |
|
20 |
|
30 |
|
40 |
The test statistic is calculated according to this formula: z = (x -µ)/(? / (n)1/2 ). Here x=1900, µ=1000, ?=24, n=576, if we plug the numbers into the formula we would have z = (1020 -1000)/(24 / (576)1/2 ) which is equal to 20
The answer is C
9.Soru
In a market, a chef selects the first 5 vegetables he sees in the fresh vegetable boxes as her test samples. Which type of sampling method does the chef use?
|
systematic |
|
convenience |
|
quota |
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stratified |
|
snowball |
A convenience sample involves a group of individuals that is ready and available. It is also called availability sampling method. pg. 13. Correct answer is B.
10.Soru
Which one of the following is not one of the reasons of sampling?
|
Cost |
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Time |
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Average |
|
Accuracy |
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Destructive tests |
Reasons Of Sampling
When we try to obtain some information about the characteristics of a population there are important reasons why we use a sample instead of a census. The main reasons for sampling can be categorised by the following topics:
Cost
Every project has a limited funding.
Time
A sampling survey often provides more timely information than a census, because fewer data have to be collected and analysed. Thus, the required information can be achieved quickly.
Accuracy
While a census data is gathered, many unexpected problems may affect the accuracy of the results such as recording errors, copying errors, false recordings by interviewers etc. So, while working with census data, we may inadvertently come across with a figure for a population parameter being further away than the actual value. With a good sampling procedure using good sampling methods and by choosing random observations, actually we can be very close to the true value of the population parameter.
Physical Impossibility
Some populations are uncountable or infinite to conduct a census. In this situation, it is impossible to consider all the elements of a population. Thus, a sample is necessary to obtain information from a population.
Destructive Tests
If a test includes the destruction of an item or product, sampling should be used. For example, when a car manufacturer would like to get a safety rating on their cars, they send a selection of cars (3 to 5 cars) to the safety agency for testing and these cars goes under different test including a crash which demolishes the car.
11.Soru
What is the third step of hypothesis testing?
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Identify the test statistic |
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Take a sample and make the decision |
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Select a level of significance |
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State null and alternate hypotheses |
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Select a level of significance |
To test the claims made about the population parameters or in other words to test the statistical expressions the following steps can be followed:
Step 1: State null and alternate hypotheses
Step 2: Select a level of significance
Step 3: Identify the test statistic
Step 4: Formulate a decision rule
Step 5: Take a sample and make the decision
12.Soru
The frequency of recovery from illness after therapy A in a sample of 640 is 160. What is the point estimate of population proportion for recovery from illness?
|
0.95 |
|
0.90 |
|
0.64 |
|
0.25 |
|
0.16 |
x = 160 / 640 = 0.25. pg. 25. Correct answer is D.
13.Soru
I. The null hypothesis defines what the decision maker’s conclusion is if he/she accepts the alternative hypothesis.
II. The null hypothesis H0 is a statistical statement which specifies that there is a specific value of a population parameter.
III. The alternative hypothesis H1 specifies that there is a difference between the value of a population parameter and a certain value.
Which of the given statements can be said about the null and alternative hypotheses?
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Only I |
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Only II |
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I and II |
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I and III |
|
II and III |
The null hypothesis H0 is a statistical statement which specifies that there is a specific value of a population parameter. Generally thought as the status quo. It is what you already know about the population parameter. On the other hand, the alternative hypothesis H1 specifies that there is a difference between the value of a population parameter and a certain value. Alternative hypothesis is also called as research hypothesis since the alternative hypothesis defines what the decision maker’s conclusion is if he/she rejects the null hypothesis.
The answer is E.
14.Soru
A new mobile device power bank’s charging time is 5 hours. 50 power banks are selected and tested for their charging time. The average charging time of these power banks is 5.05 hours. It’s assumed that the power bank charging time is normally distributed with a standard deviation as ? = 0.2 hours.
What is the sample size (n) according to the situation above?
|
5 |
|
0.5 |
|
5.5 |
|
50 |
|
0.2 |
A random sample of 50 power banks is selected and tested for their charging time. The sample size (n) is 50. The correct answer is D.
15.Soru
A chocolate factory is examining the sales of their new brand chocolates in two nearby cities. The number of chocolates sold in city 1 is 300 (n1) and 120 of the chocolates were their new brand chocolates. On the other hand, in the city 2, 240(n2) of the sold chocalates, 150 of them were their new brand chocolates. What is the test statistics? ([(1/300) + (1/240)] can be assumed to be equal to 0.25)
|
-2.9 |
|
-1.9 |
|
-1.6 |
|
-1.3 |
|
-0.9 |
n1 =300, x1 = 120 then p1 = x1/n1= 120/300= 0.4
n2 =240, x1 = 150 then p2 = x2/n2= 150/240= 0.625
p = (x1 + x2)/(n1 + n2) = (120 + 150)/(240 + 300) =0.5
Then, z-test is used to test the difference between two proportions p1 and p2 and the test statistic is as follows: The numarator is 0.4 - 0.625 = -0.225.
0.5x(1-0.5)=0.25, [(1/300)+(1/600)] is assumed to be equal to 0.25 therefore the denominator is 0.25. This yields to z = -0.225/0.25 = -0.9
The answer is E.
16.Soru
Interval estimation : the sample arithmetic mean is 26 and the upper limit of the confidence interval is 33, then what is the lower limit of the confidence interval?
|
23 |
|
21 |
|
20 |
|
19 |
|
17 |
26 = (x + 33) / 2 ; x = 19. pg. 33. Correct answer is D.
17.Soru
In a problem, the variance between samples is 350 and variance within samples is 70. What is the test statistic F according to this information?
|
0,5 |
|
5 |
|
15 |
|
0,7 |
|
0,35 |
The test statistic for a one-way ANOVA test is the ratio of two variances; namely the variance between samples (MSB) and variance within samples (MSW). Then, the test statistic F can be obtained as follows, F = MSB / MSW.
Then,
F = 350/70 = 5 . The correct answer is B.
18.Soru
I. The alternative hypothesis can be expressed in three different ways according to the purpose of the research question.
II. H1: ? ? ?0 A hypothesis test whose alternative hypothesis (H1) has this form named as the one-tailed test or one-sided alternative hypothesis.
III. Right-tailed and left tailed hypothesis tests are also called a two-tailed test or two-sided alternative hypothesis.
Which of these statements about hypothesis testing are true?
|
Only I |
|
Only II |
|
I and II |
|
I and III |
|
II and III |
I. The alternative hypothesis can be expressed in three different ways according to the purpose of the research question. (True)
II. H1: ? ? ?0 A hypothesis test whose alternative hypothesis (H1) has this form named as the one-tailed test or one-sided alternative hypothesis. (False, H1: ? ? ?0 A hypothesis test whose alternative hypothesis (H1) has this form named as the two-tailed test or two-sided alternative hypothesis.)
III. Right-tailed and left tailed hypothesis tests are also called a two-tailed test or two-sided alternative hypothesis. (False, Right-tailed and left tailed hypothesis tests are also called a one-tailed test or one-sided alternative hypothesis.)
The answer is A.
19.Soru
____________________________ is the probability distribution of all possible sample means that can be created from a population with a fixed sample size of n.
____________________________ is the probability distribution of all possible sample means that can be created from a population with a fixed sample size of n.
|
The sampling distribution of the sample variance |
|
The sampling distribution of the sample standard deviation |
|
The sampling distribution of the sample mean |
|
The sampling distribution of the sample median |
|
The sampling distribution of the sample mode |
The sampling distribution of the sample mean is the probability distribution of all possible sample means that can be created from a population with a fixed sample size of n.
20.Soru
Which of the following is NOT a statistical hypothesis?
|
The mean age of students in a classroom is 26.5 years. |
|
The variance of thefuel consumption of a certain model car under various road and traffic condition is 0.76 litres in 100 kilometres. |
|
The battery manufacturer claims that the average number of charge cycle is about 900 charge cycles for the specific type of rechargeable batteries |
|
The proportion of people wearing eyeglasses is almost four times higher than that the proportion of the contact lens users. |
|
The students who study in a library recall more information than students who study at home. |
In general, a hypothesis is a proposition for the specific situation encountered. Conversely a statistical hypothesis that specifies a single value for a population parameter and validity of this parameter is based on generating statistics which can be investigated by sampling distribution of the concerned information. In other words, statistical hypothesis utilizes sample statistics to determine whether a hypothesis is true or not. The correct answer is E.
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