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Exam 2021 Statistics january, Exámenes de Estadística

Exam from ARA class, Statistics with Manuel

Tipo: Exámenes

2020/2021

Subido el 19/01/2022

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We will only consider those answers that are written clearly in the box below. You can leave
answered questions; they are not considered errors. Each incorrect answer subtracts half correct
response.
Write ONE answer for each question (A, B or C)
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CASE 1: A researcher wanted to examine whether the educational level of participants (3
levels of the independent variable) has an effect on sustained attention. Three hundred people
between 30 and 35 years old were recruited, 100 with primary education, 100 with
secondary education, and 100 with university studies. The participants had to detect, in
1000 trials, the letter F in matrices containing (or not) the letter E on a computer screen.
The researcher measured the reaction time in each trial (in milliseconds) as a marker of
attention.
1. The study described in CASE 1 is:
a) Correlational-Observational, because this research follows the usual correlational-
observational approach in which the Pearson coefficient is computed.
b) Experimental, because the independent variable is directly manipulated and the
logic of the research is to examine its impact on the dependent variable.
c) Quasi-experimental, because the three groups of the independent variable have
been formed naturally rather than by random assignment.
2. (CASE 1) What type of variable is "Educational Level"?
a) Ordinal
b) Qualitative (nominal)
c) Quantitative (discrete)
3. (CASE 1) What type of variable is "Reaction Time"?
a) Quantitative (continuous)
b) Quantitative (discrete)
c) Ordinal
4. What measure of association would you use to assess the relationship between the
variables "Gender" (male, female, other) and "Religion" (Christian, Muslim, other
religions, non-believer)?
a) Pearson Correlation
b) Spearman Correlation
c) Cramer's V Correlation
5. If the relationship between two variables X and Y is very high (e.g., a Pearson's
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We will only consider those answers that are written clearly in the box below. You can leave answered questions; they are not considered errors. Each incorrect answer subtracts half correct response. Write ONE answer for each question (A, B or C)

CASE 1: A researcher wanted to examine whether the educational level of participants ( levels of the independent variable) has an effect on sustained attention. Three hundred people between 30 and 35 years old were recruited, 100 with primary education, 100 with secondary education, and 100 with university studies. The participants had to detect, in 1000 trials, the letter F in matrices containing (or not) the letter E on a computer screen. The researcher measured the reaction time in each trial (in milliseconds) as a marker of attention.

1. The study described in CASE 1 is: a) Correlational-Observational, because this research follows the usual correlational- observational approach in which the Pearson coefficient is computed. b) Experimental, because the independent variable is directly manipulated and the logic of the research is to examine its impact on the dependent variable. c) Quasi-experimental, because the three groups of the independent variable have been formed naturally rather than by random assignment. 2. (CASE 1) What type of variable is "Educational Level"? a) Ordinal b) Qualitative (nominal) c) Quantitative (discrete) 3. (CASE 1) What type of variable is "Reaction Time"? a) Quantitative (continuous) b) Quantitative (discrete) c) Ordinal 4. What measure of association would you use to assess the relationship between the variables "Gender" (male, female, other) and "Religion" (Christian, Muslim, other religions, non-believer)? a) Pearson Correlation b) Spearman Correlation c) Cramer's V Correlation 5. If the relationship between two variables X and Y is very high (e.g., a Pearson's

coefficient of 0.96), we can conclude that a) The variable X has a causal relationship on the variable Y b) Both variables covariate very highly c) The variable X follows the normal distribution

6. If we have the JASP (or SPSS) output of a simple regression equation and we want to know the Pearson correlation coefficient (i.e., r), the preferred option is a) To only look at R—the slope in standardized scores does not provide the sign b) To only look at the slope in standardized scores (R does not provide the sign). c) To look at R or the slope in standardized scores (i.e., both will provide the same value). 7. Peter is in the 99th percentile on a standardized psychological test that measures anxiety. From the following range, what z-score is most likely to correspond to him? a) z-score of approximately 0. b) z-score less than 0. c) z-score greater than 0. 8. If we have a symmetric distribution that has more density (height) in the center and at the ends than the normal distribution, we will presumably be looking at a a) Mesokurtic distribution b) Platikurtic distribution c) Leptokurtic distribution

OUTPUT 1 (Math, Chemistry and Technical Drawing grades of 224 students)

Descriptive Statistics

MATHEMATICS CHEMISTRY DRAWING

Valid 224 224 224

Mean 8.321 8.089 5.

Median 9.000 8.000 6.

Std. Deviation XXX XXX XXX

IQR XXX XXX XXX

Skewness -0.996 -0.638 -0.

Std. Error of Skewness 0.163 0.163 0.

Kurtosis 0.673 -0.392 0.

Std. Error of Kurtosis 0.324 0.324 0.

Minimum 2.000 3.000 3.

Maximum 10.000 10.000 8.

25th percentile 7.000 7.000 5.

50th percentile 9.000 8.000 6.

75th percentile 10.000 10.000 6.

9. (OUTPUT 1) Which of the 3 variables shows the least degree of asymmetry? a) Mathematics b) Technical Drawing c) All 3 show exactly the same degree of asymmetry

14. (OUTPUT 2) What is the percentage of variance of “Technical Drawing” can explain the regression equation? a) Approximately 61% b) Approximately 37% c) Approximately 69% 15. (OUTPUT 2) Do you think there could have been collinearity problems in the regression equation? a) Not particularly serious, the highest VIF is 1. b) There are serious problems because all VIFs are over 1. c) There are serious problems because each VIF offers a different value. 16. (OUTPUT 2). Using the regression equation, what score would you predict in “Technical Drawing” (direct scores) for someone who has a 0 in Mathematics, Foreign Language and Spanish Language? a) 2. b) 5. c) 0. 17. What theoretical distribution has degrees of freedom in the numerator and the denominator? a) chi-square b) Fisher’s F c) Student t 18. We have a probability density distribution in a continuous random variable X, where f(x)=1.5 for a given value of X. Is that possible? a) Yes, because f(x) is not a probability. b) No, because f(x) is bounded between -1 and 1. c) No, because f(x) is bounded between 0 and 1. 19. If we answer a multiple-choice exam composed of 20 questions, each with three alternatives (one correct and two incorrect), totally at random, what is the probability of getting at least one correct answer? a) 1-(2/3)^20 b) 1-(1/3)^20 c) (1/3) + (2/3)^19 20. The greater the number of degrees of freedom, the chi-square distribution a) is more and more similar to a standardized normal distribution N(0,1) b) decreases its positive asymmetry c) increases its positive asymmetry