Midterm

• Exam covers multiple choice, select all that apply, matching, fill in the blank, short answer, graph interpretation, and code interpretation items.
• Responses should be within the provided boxes, handwriting must be clear and legible.
• No items require long answers.
• If an item cannot be solved, mark it for review and return to it later.
• Writing the student ID number on the top of each page and ensuring written answers are legible will earn 3 extra credit points.

Question 1

• Ronald Fisher is most closely associated with the p = .05 threshold for significance.

Question 2

• Conditions for a same to be a good model of its population:
  • Data are normally distributed.
  • Sample is extremely large.
  • Data was sampled independently.
  • Sample is representative of the population.

Question 3

• If a set of data is perfectly normally distributed, the probability of randomly drawing a score that falls within 1 standard deviation of the mean needs to be determined.

Question 4

• If the results of a study are genuinely representative of a population, the true population mean will lie within the boundaries of the confidence interval.

Question 5

• Python code is provided.
• Identify which of the following its function preforms:
  • Produces a histogram
  • Resamples existing data
  • Generates Monte Carlo data
  • Defines a bootstrap function
  • Calls a function
  • Creates an array of individual scores

Question 6

• The study examples includes a non-directional hypothesis:
  • Participants in a study of yoga versus mindfulness meditation will report similar levels of anxiety.

Question 7

• Determine what happens to resulting data in a Monte Carlo simulation if the standard deviation is changed from a smaller value to a larger value.

Question 8 and 9

• Dr. Murky is evaluating the effectiveness of two new aftershave advertisements in 150 pharmacies and supermarkets in London, Ontario.
• 50% of locations are randomly selected to display Ad 1, with the rest carrying Ad 2 for one week.
• The plot shows the total number of product purchased with the advertisement present.
• Report the averages for Advertisement 1 and Advertisement 2 to the nearest whole number based on the data.
• Identify which statistic the average is showing:
  • Arithmetic Mean
  • Median
  • Mode
  • Geometric Mean

Question 10

• Determine if the two advertisements differ, in terms of the number of sales they promoted and why or why not.

Question 11

• Identify the formula that Dr. Murky should use to calculate the variance of each sample.

Question 12

• Rank order the elements of the study from most (rank = 1) to least (rank = 5) important using the boxes beside each item to provide rankings:
  • The two advertisements and any differences between them
  • The calculated statistics based on the sample data
  • How the ads were selected for placement at each location
  • The number of days the trial ran
  • The participant sample (people in the London, Ontario area who buy men's aftershave)

Question 13

• Based on a provided sample distribution, identify which point estimator is likely to be most efficient for the data presented.

Question 14

• Provide a single sentence to explain the answer given in question 13.

Question 15

• If p(event 1 | event 2) = p(event 1), determine which is true:
  • The two events are related to one another
  • The two events are independent
  • The two events are complementary
  • The probability of event 1 depends on the probability of event 2

Question 16

• Determine what would happen to the resulting data in a bootstrap simulation assuming the number of resampled participants is reduced.

Question 17

• When conducting significance tests one would:
  • Test the research hypothesis to determine if it is true.
  • Always use a statistical threshold of p = .05.
  • Presume that the null hypothesis is true.
  • Presume a cause-and-effect relationship between the independent and dependent variables.

Question 18

• Describe the standard error of the mean.

Question 19

• List the assumptions a researcher must make to calculate the 95% confidence interval using a formula, rather than a bootstrap approach.

Question 20

• Identify the biased statistics:
  • Mean
  • Median
  • Mode
  • Variance
  • Standard Deviation

Question 21

• Event X and Event Y are disjoint evernts
• Determine what is the probability of both events occurring together?

Question 22

• Choose what is a good descriptor for the standard deviation of a sample around it's mean:
  • The interval within which the mean is 68% likely to lie.
  • The average squared deviation of scores in the sample, in squared units.
  • The average deviation of scores in the sample, in original units.
  • The population parameter sigma.

Question 23

• Study: California study observed whether drivers stopped for pedestrians at crosswalks/intersections or sped through, categorized by luxury (BMW, Audi, Porsche) vs. non-luxury brands (Nissan, Kia, Toyota).
• Observations noted between 11 AM and 1 PM over 14 day period.
• Numerator & denominator are required for the following questions, not the completed calculations.
• What proportion of the cars observed in the study were luxury brands?

Question 24

• What is the probability of stopping for approaching pedestrians, given that the car is a luxury vehicle?

Question 25

• What is the probability of driving a non-luxury vehicle and not stopping for approaching pedestrians?

Question 26

• Describe what a Type II error is.
• What is the probability of making one in the research?

Question 27

• Select whether any of the following describe a random process:
  • The month of March 2023 will follow the month of February 2023.
  • The number of items you will get correct on this exam.
  • That it will snow tomorrow.
  • Flipping heads on a coin with two heads sides.

Question 28

• Researcher examines whether a new math program helps kids learn.
• 200 3rd grade children sampled, 100 are in the intervention and the remainder are enrolled in the standard grade 3 curriculum.
• After the school year, children take a post-test.
• A histogram displays improvement by either change scores (post-test - pre-test) with high scores reflecting more improvement.
• Data are not normally distributed, so a randomization test must examine the study outcome.
• Determine the critical element in the logic of the randomization test and why it works:
  • If the obtained p-value is smaller than 0.05, the null hypothesis can be rejected.
  • The design is experimental because the participants have been randomly assigned to groups.
  • The originally obtained statistic is compared to the distribution of obtained values.
  • If the null hypothesis is true, participants can be reassigned to groups at random.

Question 29

• In the experiment's design, the researcher is investigating the differences between both pre-test and post-test.
• Is the hypothesis directional or non-directional?

Question 30

• The researcher conducts the randomization test, re-randomizing the data and computing the statistic 1000 times.
• Determine which histogram should be used.

Question 31

• Explain the reasoning behind the choice.

Question 32

• His test statistic is 2.83.
• Describe the statistical decision based on the selected histogram.

Question 33

• Identify which of the following snippets of python code most probably produced the data for the histogram?
• The data in the adjacent graph are from a Monte Carlo simulation.

Question 34

• Based on what one learned about confidence intervals, interpret the results shown in the provided figure.

Question 35

• Select the best distribution for the adjacent data plot:
  • Uniform
  • Binomial
  • Gaussian
  • Irregular
  • The original distribution cannot be determined from this plot

Question 36

• Explain the reasoning for the choice from the previous item.

Question 37

• Select why not to use use a 100% confidence interval:
  • There is a chance that we would miss the true population mean due to sampling error.
  • The interval would be so wide that it would become uninformative.
  • It is not traditional to use a 100% confidence interval.
  • The confidence interval formula does not allow for this.

Question 38

• Match the distribution with its most likely descriptor (not all descriptors will be used):
  • Platykurtic
  • Normal
  • Binomial
  • Positively Skewed
  • Negatively Skewed

Question 39

• Car thieves are operating near the UWO campus!
• Last week, three cars were reported stolen and the police are investigating these crimes.
• Each crime has two possible, the outcome (the car is recovered as 'R' or the car missing 'L')
• Determine which options show the complete sample space for the results of this investigation:
  • {R, R, R, L, L, L}
  • {RRR, RRL, RLL, LLL}
  • {RRR, RRL, RLR, RLL, LRR, LRL, LLR, LLL}
  • None of these options accurately describe the sample space.

Question 40

• What is the probability that exactly one car will be recovered?
• Show the correct numerator and denominator without completing the calculation.

Exam guidelines covering multiple-choice, matching, and short-answer questions. Focus on clear handwriting and time management. Key topics include Ronald Fisher's significance threshold and conditions for a good statistical model.