Statistics 1A - RUG - Psychology - B1 - Practice exam 2018/2019

Questions

Question 1

If Z is standard normally distributed, what is the value of z for which P(Z>z)=0.05?

1. -0.5199
2. 0.5199
3. 1.96
4. 1.645

Question 2

The table below contains 10 scores on a variable. There is one clear outlier, displayed in the table in blue. What happens if we were to remove this outlier?

1. The mean will increase, but the median will stay the same
2. The median will increase, but the mean will stay the same
3. The mean and the median will increase
4. The mean and the median will stay the same

Question 3

The diagram below represents a density curve of variable X.

Which of the statements below is correct?

1. The mode of X is equal to zero
2. The distribution of X is skewed to the left
3. The mean and the median of X seem to be equal
4. The distribution of X is a unimodal distribution

Question 4

Belgium has two official languages: French and Dutch. Suppose 60% of the Belgian population speaks Dutch and 40% speaks French. Event A is the event that two randomly selected people from Belgium speak the same language. What is the complement of event A?

1. 0.52
2. 0.48
3. {Dutch, French}
4. {(Dutch, French), (French, Dutch)}

Question 5

Which statement below about voluntary response sample is correct?

1. Voluntary response samples are not susceptible to bias
2. A voluntary response sample contains people that have volunteered to take part in the study
3. Both A and B are correct
4. Neither A and B are correct

Question 6

Grades on the statistics 1A exam are notmally distributed with a mean of 5.5 and a standard deviation of 2. Which percentage of students has scored higher than 9.5 on the exam?

1. 2.5%
2. 5.0%
3. 95%
4. 97.5%

Question 7

In a given population the preparation time for an exam is normally distributed with μ = 115 hours and σ = 3 hours. What percentage of people from this population has a preparation time between 115 and 120 hours?

1. Approximately 45%
2. Approximately 50%
3. Approximately 55%
4. Approximately 95%

Question 8

A researcher would like to predict for both men and women the occurences of obsessive compulsive behavior from their score on an obsessive compulsive test. In this study the independent variable is...

1. Occurences of obsessive compulsive behavior
2. Sex
3. Probability of compulsive behavior
4. Score on the obsessive compulsive test

Question 9

A radnom sample size of n is dawn from a population with a mean μ and a standard deviation σ. The sample mean of all observations in the sample x̄ is determined. Which of the statements below about the sample mean x̄ is correct?

1. The standard deviation of x̄ will get smaller if the sample size n gets larger
2. The variance of x̄ is equal to (σ²/n)
3. The mean of x̄ is equal to the population mean μ
4. All the statements above are correct

Question 10

Fill in the dotted line, such that the statement is correct:

The distribution of a(n) ... variable describes categories and indicates the number or the percentage of cases in this category.

The missing term is

1. independent
2. dependent
3. quantitative
4. nominal

Question 11

For a given regression of Y on X it is known that the regression coefficients are a = 3 and b = 2, with regression formula ŷ = a + bx. It is also known that the standard deviation of X is equal to 4 and the standard deviation of Y is equal to 12. The correlation between X and Y is...

1. a = 46 and b = 0.6
2. a = 34 and b = 0.6
3. a = 39.33 and b = 0.066
4. a = 40.66 and b = 0.066

Question 12

What is a reasonable estimate for the correlation between X and Y in the figure below?

1. No reasonable estimate of the correlation can be provided, because no values for the axes have been provided.
2. -0.5
3. 0
4. 0.5

Question 13

Based on 254 observations you have calculated x̅ = 50 and s = 10. You would like to turn your observations into a variable with x̅ _new= 50 and s_new= 5. In order to achieve this, you apply a linear transformation with X_new= a + bX and b>0. The first observation was 40. What are a and b in the desired linear transformation and what will the value of the first observation be after applying said transformation?

1. a = -50, b = 2, and the first observation will be 30.
2. a = 0, b = 0.5, and the first observation will be 20.
3. a = 0, b = 1, and the first observation will be 40.
4. a = 25, b = 0.5, and the first observation will be 45.

Question 14

Which of the statements below concerning study designs is correct?

1. Given equal numbers of observations, results from simple random studies often display more variance than results from matched pairs designs
2. A design in which all participants are randomly allocated across treatments is called a simple random study
3. Both a and b are correct
4. Neither a nor b are correct

Question 15

The following is known about a large city: 72% of the people own a smart phone, 38% of the people own a tablet, and 29% own both a smart phone and a tablet. What is the probability that a randomly drawn person from this city owns a tablet, given that this person owns a smart phone?

1. 0.763
2. 0.528
3. 0.403
4. 0.273

Question 16

Which probability distribution below is a valid probability model for number of coin flips coming up heads for two throws with a fair coin?

4. None of the distributions above is correct.

Question 17

During the summer months, prices for a hotel room in Amsterdam are approximately normally distributed with a mean of 131.80 euros and a standard deviation of 29.12 euros. A travel organization takes a random sample of 15 hotels in Amsterdam. What is the probability that the mean price of 15 hotels is higher than 150 euros?

1. 0.9922
2. 0.7357
3. 0.2643
4. 0.0078

Question 18

It is known that 90% of all students own a cell phone. What is approximately the probability that in a random sample of 150 students, no more than 130 students own a cell phone?

1. P(Z <- 1.22)
2. P(Z <- 1.36)
3. P(Z <- 1.50)
4. None of the above alternatives are correct

Question 19

Three airline companies fly to and from the airport Namulonge. Airline A transports 50% of all passengers, airline B transports 30% of all passengers, and airline C transports 20% of all passengers. Every airline company is responsible for their own security. The probability that a passenger gets detected with a weapon by airlines A, B, and C are 0.9, 0.5, and 0.4, respectively. What is the probability that a passenger booked a flight with airline A, given that they were detected with a weapon?

1. 0.45
2. 0.66
3. 0.68
4. There is insufficient infromation to answer this question.

Question 20

A sampling distribution of a statistic is...

1. The mechanism that ensures randomization is effective
2. The way in which people in samples of a statistic are distributed
3. The distribution of scores on a variable in a sample
4. The distribution of values a statistic can take in all potential random samples from a population

Question 21

The management department of a company has an outstanding position for a job. Data of 410 potential candidates have been collected and are displayed in the table below

1. 0.198
2. 0.241
3. 0.293
4. 0.676

Question 22

A popular website among US students is www.studentinfo.com, it contains information about job offers in the US and abroad. The website’s management claims that 50% of all US students knows of the existence of this website. You decide to take a random sample of 10 US students and ask them if they know about this website. Of the 10 students you sampled, 2 know about the website. If the management of this website is correct in their assertion that 50% of all US students knows this website, what is the probability that exactly 2 students know this website in a random sample of 10 students?

1. 0.244
2. 0.115
3. 0.055
4. 0.044

Question 23

X is a binomially distributed variable with p = 0.35. What is the sample size necessary to obtain a standard deviation of the sample size proportion p̂ = (x/n) of no higher than 0.04?

1. 6
2. 33
3. 143
4. None of the above alternatives is correct

Question 24

We have access to scores of 60 participants. We know that the variance of X is equal to 4, the variance of Y is equal to 9, and the correlation between X and Y is equal to 0.8. What is the covariance between X and Y?

1. 1.2
2. 4.8
3. 5.4
4. 28.8

Question 25

Suppose that scores on a variable are perfectly normally distributed. What is the most efficient way (i.e., with the least numbers necessary) to fully describe these scores?

1. The mean and standard deviation
2. The median and the interquartile range
3. The five-number summary
4. The mean combined with the five-number summary

Question 26

The histogram below is a display of the distribution of a population with mean μ = 4 and variance σ² = 2 = 8

Suppose a random sample of 150 observations is drawn from this population and the sample mean is calculated. Which of the statements below regarding the sampling distribution of the sample mean is incorrect?

1. The standard deviation of the sample means is 0.23
2. The sampling distribution of the sample means will be approximately normally distributed
3. As the histogram is skewed right, the sampling distribution of sample means will also be skewed to the right
4. Despite the fact that the histogram is skewed to the right, the sampling distribution of sample means will be approximately summetrical around 4

Question 27

A discrete random variable X has a mean μ = 15 and a standard deviation σ = 4. A constant value 8 is added to X to create a new variable Y: Y = X + 8. What is the mean of Y?

1. 4
2. 15
3. 23
4. It is not possible to calculate the mean of Y without knowing the probability distribution of X and Y

Question 28

A regression analysis conducted in SPSS yielded the following output

For the regression formula ŷ = a + bx, what are the values of a and b?

1. a = 0.027 and b = 0.837
2. a = 0.324 and b = 60.811
3. a = 0.837 and b = 0.027
4. a = 60.811 and b = 0.324

Question 29

Scores on a test are normally distributed with mean 100 and standard deviation 10. What score do you need to get to belong to the 7% who score highest on this test?

1. About 85.2 or lower
2. About 85.2 or higher
3. About 114.80 or lower
4. About 114.80 or higher

Question 30

For a given regression of Y on X it is known that the regression coefficients are a = 3 and b = 2, with regression formula ŷ = a + bx. It is also known that the standard deviation of X is equal to 4 and the standard deviation of Y is equal to 12. The correlation between X and Y is...

1. 1/3
2. 2/3
3. 4/6
4. 2/12

Question 31

Which statement below about correlation coefficients r XY is correct? If all x-values are divided by 10 AND all y-values increase by 5, then...

1. r_XY does not change
2. r_XY becomes smaller
3. r_XY becomes larger
4. it is unclear what happens to r_XY without additional information

Question 32

A large number of stimuli was judged by two raters on a certain trait. The ratings of the two judges are given as scores on variables X and Y. Furthermore, it is known that Kendall’s tau between X and Y is 1. What does this mean?

1. There is perfect correspondence in the order of the ratings of the two judges
2. The five-number summaries of both judges are equal
3. Scores on X and Y are identical
4. There is a perfect linear relationship between the ratings of the two judges

Question 33

A random poll in the Netherlands was conducting on 2,000 adults. This is approximately 1 out of 6,000 adults in the Netherlands. The US population consists of approximately 18 times as many adults as the Dutch population. In one wanted to conduct a poll in the US that is equally reliable to the poll that was conducted in the Netherlands, how large should that US poll be?

1. 2,000
2. 5,400
3. 12,000
4. 36,000

Question 34

When figure skaters choose a skating partner, it is important that their body weights are compatible. For male figure skaters (X) the mean weight is 77kg with a standard deviation of 4. For female figure skaters (Y) the mean weight is 49kg with a standard deviation of 3. The correlation between X and Y is 0.77. What is the standard deviation of the random variable W = X – Y?

1. 2.55
2. 2.65
3. 6.52
4. 7.00

Question 35

It is known that 90% of all students own a cell phone. A random sample of 15 students from a large university is drawn. What is the standard deviation of the number of students that owns a cell phone for a random sample of 15 students?

1. 0.06
2. 0.08
3. 1.16
4. 1.35

Question 36

A researcher conducts a regression analysis in which he wants to predict Y from X. Displayed below is an incomplete part of the SPSS output.

Based on this output, which conclusion is correct?

1. The researcher can with 44.9% certainty predict Y from X
2. The correlation between X and Y is 0.20
3. The correlation between X and Y could be negative
4. None of the statements above is correct

Answers

Question 1

D

Question 2

A

Question 3

C

Question 4

D

Question 5

B

Question 6

A

Question 7

A

Question 8

D

Question 9

D

Question 10

D

Question 11

B

Question 12

C

Question 13

D

Question 14

C

Question 15

C

Question 16

C

Question 17

D

Question 18

B

Question 19

B

Question 20

D

Question 21

B

Question 22

D

Question 23

C

Question 24

B

Question 25

A

Question 26

C

Question 27

C

Question 28

D

Question 29

D

Question 30

B

Question 31

A

Question 32

A

Question 33

A

Question 34

A

Question 35

C

Question 36
C