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QUIZ 1 Exploring Data 1 A researcher wants to measure physical height in as much detail as possible. Which level of measurement does s/he employ? Answer: Ratio level 2 You conduct a study on eye color and you question 550 people. 110 of them have brown eyes and 44% of them have blue eyes. What percentage of the people you questioned has blue or brown eyes? [Your answer should consist of just the number, no additional characters - so if you think the answer is 41% enter the number 41] Answer: 64 3 In which situation is a bar graph preferred over a pie chart? Answer: When the number of categories in the data is high. 4 Ten students completed an exam. Their scores were: 5, 7, 2, 1, 3, 4, 8, 8, 6, 6. What is the interquartile range (IQR)? Answer: 4

5 A researcher wants to know what people in Amsterdam think of football. He asks ten people to rate their attitude towards football on a scale from 0 (don't like football at all) to 10 (like football a lot). The ratings are as follows: 1, 10, 6, 9, 2, 5, 6, 6, 5, 10. What is the standard deviation? Answer: 3,1 6 You find a z-score of -1.99. Which statement(s) is/are true? Answer: The score falls below the mean score. The score lies almost two standard deviations from the mean. 7 Which of the following statements is true? Answer: Both statements are false. 8 The grades for a statistics exam are as follows: 3, 5, 5, 6, 7.5, 6, 5, 1, 10, 4. Which score is an outlier? (Use the interquartile range (IQR).) Answer: 10 9 How many goals have the top strikers of the Dutch Eredivisie football competition scored? We look at 10 strikers and obtained the following information: 12, 10, 11, 12, 11, 14, 15, 18, 21, 11. The (1) ... of the dataset equals 12, the mean equals (2) ... and the (3) ... equals 11. The standard deviation equals (4) ... Fill in the right words/numbers on the dots. Answer: (1) Median, (2) 13.5, (3) Mode, (4) 3.57 10 What is true about a variance of zero? (Multiple answers possible.) • There is no variability in the scores: everybody has the same score. • The standard deviation equals zero as well. 11 What is the difference between variables and constants? Answer: Variables vary across cases; constants do not vary. --------------------------------------------------------------------------------------------------------------------------------------------------

QUIZ 2 Correlation and Regression 1. You want to visualize the results of a study. When assessing only one ordinal or nominal variable it is sufficient to use a (1) .... When looking at the relationship between two of these ordinal or nominal variables you'd better use a (2) .... When you're assessing the correlation between two continuous variables it's best to use a (3) ... Fill in the right words on the dots. Answer: (1) Contingency table, (2) Scatterplot, (3) Frequency table 2. Which statement(s) about correlations is/are right? I. When dealing with a positive Pearson's r, the line goes up. II. When the observations cluster around a straight line we're dealing with a linear relation between the variables. III. The steeper the line, the smaller the correlation. Answer: Statement I and II are true, statement III is false.

3. You've collected the following data about the amount of chocolate people eat and how happy these people are. Amount of chocolate bars a week: 2, 4, 1.5, 2, 3. Grades for happiness: 7, 3, 8, 8, 6. (Note, the numbers are in the right order so person one eats 2 chocolate bars and scores her happiness with a 7.) Compute the Pearson's r. Answer: -0.96 4. You've investigated how eating chocolate bars influences a student's grades. You've done this by asking people to keep track of their chocolate intake (in bars per week) and by assessing their exam results one day later. Which statement(s) about the regression line y-hat = 0.66x + 1.99 is/are true? Answer: If you eat one more chocolate bar a week, your grade becomes 0.66 higher. 5. A professor uses the following formula to grade a statistics exam: y-hat = 0.5 + 0.53x. After obtaining the results the professor realizes that the grades are very low, so he might have been too strict. He decides to level up all results by one point. What will be the new grading equation? Answer: y-hat = 1.5 + 0.53x 6. What is the explained variance? And how can you measure it? Answer: The explained variance is the percentage of the variance in the dependent variable that can be explained using the formula of the regression line. You can measure this with r-squared. 7. You want to know how much of the variance in your dependent variable Y is explained by your independent variable X. Determine for the following three cases how much variance is explained and arrange the cases in ascending order (from lower to higher explained variance). Answer: (2) (1) (3)

8. A teacher asks his students to fill in a form about how many cigarettes they smoke every week and how much they weigh. After obtaining the results he makes a scatterplot and analyses the datapoints. He computes the Pearson's r to assess the correlation. He finds a correlation of .80. He concludes that smoking more cigarettes causes high body weight. What is wrong with this analysis? Answer: He concludes that smoking causes high body weight. This is not possible after having conducted a regression analysis. 9. What can you conclude about a Pearson's r that is bigger than 1? Answer: This is impossible. Correlations are always between -1 and 1. 10. Why do you use squared residuals when computing the regression line? Answer: Because the residuals can cancel each other out (i.e. their sum equals zero).

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QUIZ 3 Probability 1. Your friend told you about someone really smart who made a good deal with the bank regarding his/her mortgage and who knows everything about the financial crisis that started in 2008. Which of the following statements is more likely? Answer: Statement I is more likely. 2. You roll a dice five times. The outcomes are: 6 6 6 6 6. Then you repeat this and you find: 1 4 3 5 2. Which of the following outcomes is most likely? Answer: Both outcomes are equally likely 3. Imagine you're at the beach. You're really thirsty and decide to go to a beach stand to get some coke. When you arrive, you see there's a queue consisting of two girls and one boy. Unfortunately the stand has only one coke left. You've learned that three in ten girls drink coke and 60 percent of boys drink coke. How likely is it that you will get the coke? Answer: 0.196 4. You ask a couple of people at the beach what they think about the seagulls. You propose them the statement: Seagulls are annoying. Their responses are as follows: 20% strongly agree, 13% agree, 12% neutral, 50% disagree, 5% strongly disagree. What is the chance of a random person responding with 'agree' given that he/she is not neutral? Answer: 0.15 5. Imagine you ask some students which subject they prefer: statistics or English. There are a lot of people that love statistics (B) and a lot of people that love English (C). However, there are also people that can't make a decision and tell you that they like both the subjects (D). When you look further into the results you realise that all the female students had a positive opinion about statistics (A). Which of these events (A, B, C, D) are disjoint? Answer: A and C & A and D 6. You collect four shells from the beach. You know that there are only three types of shells on the beach, and these shells occur in equal amounts. How many different events are possible? Answer: 81 7. Twenty people take a statistics exam. Jonas scored five out of ten and Emma scored eight out of ten. Every score (1 to 10) is equally likely. What is the chance of a random person out of the people that took the exam scoring higher than Jonas, but lower than Emma? Answer: 0.2 8. How can we define probability or chance? Answer: as a long-run relative frequency

9. You are rushing out to get to your appointment in 30 minutes. From experience you know that most of the time you travel this distance in 30 minutes. However, half of the time there is heavy traffic. In the past, there has been heavy traffic and you have made it to your appointment within 30 minutes 34% of the time. You get out on the street and see that there is heavy traffic. What is the chance you will get to your appointment on time?

Answer: 0.68 10. What is the probability of event A given event B? Answer: 0.42 11. You have a pot with 100 balls. 20 of them are red, 50 are blue and 30 are green. You decide to draw 5 balls from the pot without replacement (i.e. you don't put a ball back in the pot once it has been taken out). What is the probability of drawing five blue balls? Give your answer to 3 decimal places. Answer: 0.02814225 12. On a single train journey there is a probability of 0.4 that your ticket will be checked. You make a returnjourney, what is the probability that your ticket will be checked only once? Give your answer as a proportion, rounding to two decimal places. Answer: 0.48

13. You roll a pair of dice 20 times and record how often you get a total of 5 or 10. What is your best guess for the relative frequency that this event (a total of 5 or 10) occurs without seeing the actual data? Give your answer as a proportion, rounding to three decimal places. Answer: 0.1944444

14. The chance that the front light on your bike will fail is 0.2, the chance that your rear light will fail is 0.1 and the chance that both will fail is 0.04. What is the chance that both lights will work? (regardless of the answer you should do something about this situation of course). Give your answer as a proportion, rounding to two decimal places. Answer: 0.74

15. Which of the following statements are correct? I. A discrete random variable can take a finite number of distinct values. II. Height is an example of a continuous random variable. Answer: Both statements are correct. ----------------------------------------------------------------------------------------------------------------------------------------------------------

QUIZ 4 Probability distributions 1. The ice cream shop has problems with the delivery of the different flavours. As a consequence the shop doesn't have the same amount of flavours every day. In the following list you see the probability distribution of the different amounts of flavours. What is the mean amount of flavours the ice cream shop sells? Give your answer in two decimals. Answer: 5.57 (Indeed, the mean is calculated by the sum of the values a random variable can take times the corresponding probabilities: 4*0.14 + 5*0.35 + 6*0.31 + 7*0.2 = 5.57)

2. Which of the following statements is/are correct? I. A discrete random variable can take a finite number of distinct values. II. Height (as measured in cm) is an example of a continuous random variable. Answer: Both statements are true. 3. A researcher is interested in the time people spend online on social-media per day. She plots the probability distribution for this variable using hours as the unit, and it looks as follows:

Answer: The graph stays the same apart from the values on both axes.

4. Consider the following discrete probability distribution. What is the probability of X being higher than 2? Answer: 0.47 5. You investigate the number of earthquakes that occur in a year. You get the following outcomes: What is the variance of this random phenomenon? Give your answer in two decimals. Answer: 0.1051

6. You have a random variable X with variance 3. Now you multiply X with 2. What becomes the variance of X? Answer: 12 7. Imagine you're investigating the time people wait at traffic lights, a variable which appears to be approximately normally distributed with a mean of 1.3 minutes and a standard deviation of 0.57 minutes. Which of the following intervals contains 95% of the waiting times? Answer: 0.16 and 2.44 8. You investigate the earnings of the 2nd year students in your school. They earn on average €240,-, with a standard deviation of €90,- One person stands out, because she's a snooker champion. She makes on average €420,- a week. What is the corresponding z-score of her earnings? Give your answer in one decimal.

Answer: 2

9. On average, a proportion of 0.48 newborns are girls. What are the chances that in a family with 4 children there are exactly three daughters. Give your answer as a proportion, rounding to two decimal places. Answer: 0.2300314 10. Looking at the binomial distribution above, what would be reasonable values for the parameters of this distribution? Answer: number of trials = 20, probability of success = 0.1

11. A multiple-choice exam consists of 12 questions, each having 5 possible answers. To pass you must answer at least 8 out of 12 correctly. What are your chances of passing if you go into the exam without knowing a thing and resort to pure guessing? Give your answer as a proportion, rounding to two decimal places. Answer: .0005190451 12. The total time that I wait for busses on a long trip has the following probability density function. What is the chance that I will have to wait for more than 30 minutes? Give your answer as a proportion, rounding to two decimal places. Answer: 0.125 (The surface under the probability density function for a waiting time larger than 30 minutes is 0.025*10*0.5 = 0.125)

13. The equation above describes a normal distribution for a random variable X. It appears that the time people in the age range of 20 to 50 years spend sleeping is approximately normally distributed with a mean of 7 hours and a standard deviation of 1 hour. Can you estimate the height of this probability density curve at the mean and also give the unit of this value? Give your answer as a proportion, rounding to two decimal places. Answer: 0.4 The value of the probability density equals the value of the constant in front of e. Also note the unit of this value, which is 1/h (or 'probability per hour' if you prefer) - the unit of the standard deviation is the same as the random variable (hour).

14. For a normally distributed variable with a mean of 10 and standard deviation of 5, what is the proportion of the data with negative values? Give your answer as a proportion, rounding to three decimal places. Answer: 0.02275013 15. The following figure shows two lines that are meant to represent the cumulative probability distribution of the age of trees in a young forest where the oldest tree is 10 years. What can you say about these two cumulative distribution functions (cdfs)? Answer: Neither of these is a proper cdf. The probability of the dashed line decreases from age 6 to 7, which is impossible for a cdf; and the dotted line increments to 0.9 while it should increment to 1.0 at an age of 10 years.

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QUIZ 5 Sampling distributions 1. What is the difference between descriptive and inferential statistics? Answer: Where descriptive statistics only concerns the sample, inferential statistics concerns the underlying population. 2.

1(a), 2(b), 3(d), 4(c)

3. Which of the statement(s) is/are correct? I. A disadvantage of a telephone interview compared to a face-to-face questionnaire is that people tend to be less patient. II. The cheapest way of collecting data is an online survey. Answer: Both statements are correct.

4. How do you call the bias that can occur when not everybody from the population is included in the sampling frame? Answer: Undercoverage

5. Imagine you want to know the length of the beard of every male student in America. You know that the population mean equals 2.2 millimeters and the population standard deviation equals 0.9 millimeters. What will be the mean (in millimeters) of the sampling distribution of the sample mean (i.e., if you take an infinite number of samples)? Answer: 2.2 (The more samples you take, the closer the mean will be to the population mean.) 6. What is the central limit theorem? Answer: The central limit theorem says that the sampling distribution approximates a bell shape given that the sample is large enough.

7. Which of the following statement(s) is/are true? Answer: The sampling distribution of the sample mean is the distribution of an infinite number of sample means (with a given sample size) The larger the variability in the population distribution, the larger the variability in the sampling distribution of the sample mean.

8. Answer: This could be a population distribution or a data distribution.

9. You know that twenty percent of the people in Amsterdam describe themselves as Hipsters. You ask 400 respondents if they identify as a Hipster or not. What is the standard deviation of the sampling distribution of the sample proportion? Answer: sqrt ((0.2*0.8)/400) = 0.02

10. Which conclusion can you draw if a data distribution is very different from the corresponding population distribution (provided that the sample size is very large)? Answer: The sample is biased and does not represent the population well.

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QUIZ 6 Confidence Interval 1. You want to know how many hours of sleep new parents lose after they had their first baby. You know that the population mean equals 2.3 hours. Because you can't investigate the whole population, you take a sample of 100 people. You find an average sleep loss of 2.1 hours. What is, based on this sample, the point estimate of your population mean? Answer: 2.1 2. Which of the following statement(s) is/are correct? I. When you want to be really sure that you don't draw the wrong conclusions (e.g., when deciding about administering heavy medication or not) it is always best to use a 90% confidence interval instead of a 95% or a 99% confidence interval. II. 95% of the values under the normal distribution will fall between -1.96 and 1.96 standard deviations of the mean. Answer: Statement II is correct, statement I is incorrect. 3. Because of their sleep deprivation new parents have a hard time focusing. The average number of minutes a new parent can focus equals 3.7. The standard deviation equals 0.8. You assess how long 150 randomly selected new parents can focus and find that the mean equals 3.8 minutes and the standard deviation equals 0.5. What is the 95% confidence interval? Answer: (3.67, 3.93)

4. You've asked 55 parents if they have more than one child. It turns out that 77 in 100 parents have more than one child. Compute the 99% confidence interval. (Ignore for now that you don't have at least 15 successes and 15 failures.) Answer: (0.62, 0.92)

5. A researcher wants to investigate the driving capabilities of new parents. He doesn't know anything about the population so he decides to draw a simple random sample of 88 new parents and to make inferences based on that sample. He makes the new parents drive in a simulator and finds that, on average, they make 2.1 more accidents than people who have not become a parent recently. What are the degrees of freedom? Answer: 87

6. A researcher wants to investigate the driving capabilities of new parents. He draws a simple random sample of 88 new parents and lets them take a test in a drive simulator. He finds that, on average, they fall asleep after 2.1 hours. The standard deviation equals 0.5 hours. Compute the 90% confidence interval. Answer: (2.01, 2.19) 7. Which assumptions don't need to be satisfied for the construction of a confidence interval for a mean? Answers: The independent variable must be discrete. The sample mean must be equal to the population mean. The relationship between X and Y must be linear.

8. The following statements are about confidence intervals for proportions. Place in order from smallest to largest z-score. (1) 99%...