1. What does the test statistic tell you?

1. What does the test statistic tell you?

• It indicates how many standard errors a point estimate lies from the expected null hypothesis population value.
• It's another word for the p-value.
• It indicates whether you should use z- or t-distribution to calculate probability.
• It indicates how far from the actual population value your sample mean lies.

2. In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. You are going to select an individual from the group of students. The probability of event A is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. What is the probability of the event A’s complement?

• 0.51
• 0.26
• 0.49
• 0.74

3. Assume your null hypothesis is ? = 6. In your sample you find a value that is lower than 6. Is it 'easier' to reject the null hypothesis with a one-tailed or two-tailed test?

• A one-tailed test.
• A two-tailed test.
• This depends on the level of significance.
• This depends on the P value.

4. Someone makes the following assertion: if the sample becomes larger, then the standard deviation becomes smaller. Which of the following statements is correct?

• This assertion does not apply to any distribution.
• This assertion always applies to all distributions.
• This assertion always applies to the sample distribution and the sampling distribution.
• This assertion always applies to the sampling distribution.

5. The largest number of Oscars received by a film in year X was 4. This was different in previous years. Below is a probability distribution for the number of Oscars per Oscar winning film. What is the standard deviation of this distribution?

Number of Oscars P(x)

1 0.56

2 0.23

3 0.11

4 0.05

5 0.03

6 0.02

• 1.82
• 1.19
• 6
• 1.32

6. You draw a sample from the population of a town (n = 312) and find that of this sample, 23% are highly educated and 27% are low-educated. What is the 80% confidence interval for the proportion of highly educated people in this town?

• (0.21, 0.25)
• (0.20, 0.26)
• (0.25, 0.29)
• (0.23, 0.27)

7. What type of table is shown below?

Country GDP Gini Index

The Netherlands 850,000 25

Germany 3,500,000 30

France 2,800,000 31

Italy 2,000,000 33

• Data matrix
• Cross table
• Frequency table
• Scatterplot

8. You know that there is a strong correlation between the consumption of ice cream and body weight. The Pearson's r = 0.78. You also know that the average consumption of ice cream per week is five grams with a standard deviation of 1.5 grams. The average weight is 65 kg with a standard deviation of 15 kg. What is the formula of the regression line?

• ? = -502 + 0.078x
• ? = 7.8 + 26x
• ? = 0.078 - 502x
• ? = 26 + 7.8x

9. See the sample space below. What is the probability of event B occurring, given that event A has occurred?

• 0.09
• 0.23
• 0.82
• 0.19

10. What is a probability?

• A P-value.
• The proportion of times that something will occur in the long run.
• An uncertainty.
• The number of times that something occurs in an experiment.

11. 25% of all students find this BS exam difficult. You select four random students. What is the probability that exactly two of them find this exam difficult?

• 0.07
• 0.02
• 0.06
• 0.21

12. Various forms of bias can occur when we select a sample. What is sampling bias?

• If not everyone in the sampling frame has an equal chance to get into the sample.
• If not everyone in the population has an equal chance to enter the sampling frame.
• If not everyone in the sample actually participates in the research.
• If not everyone in the sample belongs to the population.

13. Variable A is normally distributed with ? = 12.30 and ? = 3.11. What is the probability that a randomly selected case will have a score of less than 14?

• 0.88
• 0.29
• 0.71
• 0.12

14. A random sample of 61 Basic Statistics students were asked what they thought of statistics on a scale of 0 (very stupid) to 100 (very nice). Interestingly, students seem to find statistics quite nice: the sample mean equals 83. The sample standard deviation equals 7. We know that the standard deviation in the population (all BS students) is 8. Calculate the 90% confidence interval.

• (81.53, 84.47)
• (81.24, 84.76)
• (81.32, 84.68)
• (80.99, 85.01)

15. You know that for variable A ? = 1400 and ? = 300. You also know that the variable is normally distributed. You decide to change the scores of this variable into z-scores. What is the mean and standard deviation of this new distribution?

• Mean = 1400, standard deviation = 1.
• Cannot be calculated on the basis of this information.
• Mean = 0, standard deviation = 1.
• Mean = 1400, standard deviation = 300.

16. Ten students resit the Basic Statistics exam. Their final grades are: 4, 4, 2, 9, 7, 9, 6, 4, 7, 8. What is the interquartile range?

• 2
• 8
• 4
• 7

17. Which of the following is not the explained variance?

• The degree to which the regression equation of X and Y is better at predicting the dependent variable than the average of Y.
• The percentage of variance in Y that is explained by the mean of X.
• The percentage of the variance in Y which is explained with the regression equation.
• The Pearson r squared.

18. Look at the following cross table of two ordinal variables. Is there a correlation between variable A and B?

Variable A

Variable B 1 2 3 4 Total

1 5 5 5 5 20

2 5 5 5 5 20

3 5 5 5 5 20

4 5 5 5 5 20

Total 20 20 20 20 80

• No, there is no correlation.
• Cannot be seen from the table.
• Yes, there is a positive correlation.
• Yes, there is a negative correlation.

19. Look at the table below. Calculate the Pearson's r.

Variable 1 Variable 2

Person 1 1 23

Person 2 6 48

Person 3 7 41

• 0.61
• 0.81
• 0.71
• 0.91

20. Based on a random sample of n = 2345, the 95% confidence interval of variable X is (7.25, 9.12). You expect that the mean in the population is different from 7 at ? = 0.05. What can you conclude?

• Nothing, because you have not enough data to determine that.
• The value in the population is indeed different from 7.
• You cannot reject the null hypothesis.
• This confidence interval is wrong.

21. Which of the following statements about the regression line is not correct?

• The constant indicates the place where the regression line crosses the Y-axis.
• The regression line is the line of which the sum of the residuals is the smallest.
• The regression line can run horizontally.
• The regression coefficient is the change in the Y value with 1 unit increase in the X value.

22. You’re going to draw a random sample of professional football players because you want to know what percentage have completed high school. You want to have a margin of error of up to 0.03 at a confidence level of 90%. How big should your sample be?

• Minimum 1068
• Minimum 456
• At least 30
• Minimum 748

23. 81 random elementary schools were asked for their average exam scores (sample mean = 535, sample standard deviation = 7). Calculate the 98% confidence interval.

• (533.41, 536.59)
• (533.15, 536.85)
• Not possible to calculate based on this information.
• (528.00, 542.00)

24. A type I error means that:

• The null hypothesis is true, and you do not reject the null hypothesis.
• The null hypothesis is true, and you reject the null hypothesis.
• The null hypothesis is false, and you reject the null hypothesis.
• The null hypothesis is false and cannot reject the null hypothesis.

25. You know that the heights of four people are: 156 cm, 184 cm, 172 cm and 165 cm. What is the standard deviation?

• 28
• 10.23
• 139.58
• 11.81

26. Last year the mean turnover of a group of companies was 434,000 euro. You have good reasons to expect that this year’s turnover will be higher. Your null hypothesis is therefore: ? = 434,000. Your alternative hypothesis is: ? > 430,000. You randomly sample 101 companies. The sample mean turns out to be 450,000 euro, with a standard deviation of 100,000 euro. Calculate the test statistic. Which of the following statements is correct?

• You do not reject the null hypothesis at ? = 0.05, and not at ? = 0.10.
• You reject the null hypothesis at both ? = 0.05 and ? = 0.10.
• You reject the null hypothesis at ? = 0.05, but not at ? = 0.10.
• You reject the null hypothesis at ? = 0.10, but not at ? = 0.05.

27. Film critics gave the film Basic Statistics: The Movie an average rating of 8.1 (on a scale of 0-10). The standard deviation is 0.7. You drew a random sample of n = 56 from all film critics and asked them to rate the film Boyhood with a number. What is the probability that the average rating in the sample is greater than 8.0?

• 14%
• 44%
• 86%
• 56%

28. You draw a sample from the population of Dutch voters. You do this by randomly selecting 10 voters from each municipality. What kind of sample is this?

• Stratified random
• Snowball
• Cluster random
• Convenience

29. What does the 95% confidence interval tell us?

• In 95% of cases when we sample from a population, the sample mean falls within the interval: sample mean ± 1.96 times the standard deviation of the sampling distribution.
• In 95% of cases when we sample from a population, the population mean falls within the interval: sample mean ± 1.96 times the standard deviation of the sampling distribution.
• In 95% of cases when we sample from a population, the population mean falls within the interval: sample mean ± 1.64 times the standard deviation of the sampling distribution.
• In 95% of cases when we sample from a population, the sample mean falls within the interval: sample mean ± 1.64 times the standard deviation of the sampling distribution.

30. What is a characteristic of the t-distribution?

• The t distribution has a mean of one.
• The t-distribution has the same shape as the normal distribution.
• A t-value that is multiplied with a standard error is equal to the margin of error for a confidence interval of a mean.
• The t-distribution approaches the normal distribution if it has a large standard deviation.