#### Quiz 1: Quiz: Categorical and Numerical Variables

Q1. Is the number of certain products sold in an accounting year a categorical or numerical variable?

• Numerical- Discrete
• Numerical- Continuous
• Categorical- Ordinal
• Categorical- Nominal

Q2. Is the time-share owner’s satisfaction level with the maintenance of the unit purchased (1: strongly disagree to 5: strongly agree) a numerical or categorical variable?

• Categorical- Ordinal
• Numerical- Continuous
• Categorical- Nominal
• Numerical- Discrete

Q3. Is the number of renegotiations asked by the borrower of a revolving loan a numerical or categorical variable?

• Categorical- Ordinal
• Numerical- Discrete
• Categorical- Nominal
• Numerical- Continuous

Q4. Is gender a numerical or categorical variable?

• Categorical- Nominal
• Numerical- Discrete
• Numerical- Continuous
• Categorical- Ordinal

#### Quiz 2: End of Week Quiz

Q1. A sample is the complete set of all items of interest.

• True
• False

Q2. In a random sampling every possible sample of a given size, n, has the same chance to be chosen.

• True
• False

Q3. Statistics can be used to enable fully informed decisions.

• True
• False

Q4. A parameter is a numerical measure that describes a specific characteristic of a sample.

• True
• False

Q5. Descriptive statistics focus on graphical and numerical procedures that are used to summarize and process data.

• True
• False

#### Quiz 1: Summative Questions

Q1. Given the following dataset, which measure of central tendency would be most appropriate for describing the data?

• 30 83 85 90 92
• Median
• Range
• Mean
• Mode

Q2. What would the mean of the following data be?

30 83 85 90 92

The mean is calculated by adding up all the values and dividing by the number of values:

(30 + 83 + 85 + 90 + 92) / 5 = 76

Q3. Marketing research found that there was an increase in purchases over the Christmas period in 2015 compared to 2014. Using the data below, calculate the mean percentage increase in purchases.

20.2 4.1 6.9 8.0 4.7 3.9 7.8 8.3 9.2 5.3

Mean percentage increase:

(20.2 + 4.1 + 6.9 + 8.0 + 4.7 + 3.9 + 7.8 + 8.3 + 9.2 + 5.3) / 10 = 7.84%

Q4. What is the mode of the following data?

0% 0% 8.1% 13.6% 19.4% 20.7% 10.0% 14.2%

The mode is 0%.

Q5. Given a random sample of four (x, y) pairs of data points:

(3.1,9) (3.5,13) (5,15) (4.6,11)

What is the covariance?

(3.1,9) (3.5,13) (5,15) (4.6,11)

To calculate the covariance:

Cov(x, y) = Σ[(x - x̄)(y - ȳ)] / (n - 1)

Where x̄ is the mean of x, ȳ is the mean of y, and n is the number of data points.

First, calculate the means:
x̄ = (3.1 + 3.5 + 5 + 4.6) / 4 = 4.3
ȳ = (9 + 13 + 15 + 11) / 4 = 12

Now, calculate the covariance:
Cov(x, y) = [(3.1 - 4.3)(9 - 12) + (3.5 - 4.3)(13 - 12) + (5 - 4.3)(15 - 12) + (4.6 - 4.3)(11 - 12)] / (4 - 1)
Cov(x, y) = [-3.21 + (-0.93) + 0.21 - 0.09] / 3
Cov(x, y) = -4.02 / 3 ≈ -1.34 (rounded to four decimal places)

Q6. Using the answer to the above, compute the sample correlation coefficient.

To calculate the sample correlation coefficient (r), you can use the following formula:

r = Cov(x, y) / (σx * σy)

Where:

Cov(x, y) is the covariance you calculated in the previous answer (-1.34).
σx is the standard deviation of x.
σy is the standard deviation of y.
Since you haven't provided the standard deviations of x and y, you would need those values to compute the sample correlation coefficient (r).

#### Quiz 2: End of Week Quiz

Q1. The mean is not sensitive to extreme values (outliers).

• True
• False

Q2. The range takes into account only the largest and smallest observations.

• True
• False

Q3. The skewness of a distribution depends on the degree of dispersion around the mean.

• True
• False

Q4. If Cov(x,y) < 0 , then x and y tend to move in opposite directions.

• True
• False

Q5. In a set of data, a mode always exists.

• True
• False

#### Quiz 1: Summative Questions

Q1. A seller in particular has day three HP printers and two Brother printers in his store.

Suppose that a customer comes into the store to purchase two printers. She is not interested in a particular brand — since both of them have the same operating characteristics. This is why the customer chooses the computers purely by chance. Therefore this means that: Any printer is equally likely to be selected.

What is the probability that the customer will choose one HP and one Brother printer?

2
1

Probability(HP then Brother) + Probability(Brother then HP) = (3/5) * (2/4) + (2/5) * (3/4)

Calculating this:

(3/5) * (2/4) + (2/5) * (3/4) = 6/20 + 6/20 = 12/20 = 0.6

So, the probability that the customer will choose one HP and one Brother printer is 0.6.

Q2. A company is hiring candidates for four CEO positions. Five candidates are women, and three are men.

Given that all eight candidates are equally qualified, and that every combination of male and female candidates is equally likely to be chosen, what is the probability that at least one man will be chosen?

Answer:
To find the probability that at least one man will be chosen, we can calculate the complement probability (i.e., the probability that no men are chosen) and subtract it from 1.

Probability(no man is chosen) = Probability(all women are chosen)
Number of ways to choose 4 women out of 5 / Total number of ways to choose 4 candidates out of 8

Probability(no man is chosen) = (5C4 / 8C4)

Now, we can calculate the complement probability:

Probability(at least one man is chosen) = 1 - Probability(no man is chosen)

Calculating this:

Probability(at least one man is chosen) = 1 - (5C4 / 8C4)
Probability(at least one man is chosen) = 1 - (5 / 70)

Now, simplify:

Probability(at least one man is chosen) = 1 - (1/14)
Probability(at least one man is chosen) = 13/14

So, the probability that at least one man will be chosen is 13/14.

Q3. If we throw two dice, what is the probability of getting 9 as a sum?

• \frac{1}{6}61​
• \frac{1}{9}91​
• \frac{1}{3}31​
• \frac{1}{2}21​
• The probability of getting a sum of 9 when throwing two dice is 1/12.

Q4. A mathematics class is comprised of 10 economics students and 5 statistics students. All the students in a class recently took a test.

The probability that an economics student has a mark higher than 27 is 0.2. The probability that a statistics student has a mark higher than 27 is 0.3.

If you picked a student from the class at random, what would be the probability that he or she would have a mark higher than 27?

The probability depends on whether the student is an economics student or a statistics student.

For economics students: Probability(higher than 27) = 0.2

For statistics students: Probability(higher than 27) = 0.3

Now, we need to calculate the overall probability considering the proportions of each type of student:

Probability(higher than 27) = (Proportion of economics students) * (Probability for economics students) + (Proportion of statistics students) * (Probability for statistics students)

Proportion of economics students = 10 / 15 (10 economics students out of 15 total) Proportion of statistics students = 5 / 15 (5 statistics students out of 15 total)

Now, calculate:

Probability(higher than 27) = (10/15) * 0.2 + (5/15) * 0.3

Simplify:

Probability(higher than 27) = (2/3) * 0.2 + (1/3) * 0.3

Now, calculate the probabilities:

Probability(higher than 27) = 0.4/3 + 0.3/3

Probability(higher than 27) = 0.7/3

Probability(higher than 27) ≈ 0.233 (rounded to three decimal places)

So, the probability that a randomly picked student has a mark higher than 27 is approximately 0.233.

Q5. After two midterm tests, 10% of the students passed both tests and 50% of the class passed only the first test.

What percent of those who passed the first test also passed the second test?

• 5%
• 20%
• 50%
• 100%

#### Quiz 2: End of Week Quiz

Q1. In conditional probability, if Event B has occurred, then Event A will occur

• True
• False

Q2. In a random experiment, two distinct outcomes may receive the same value.

• True
• False

Q3. The probability 𝑃𝑟(𝑋=𝑥)Pr(X=x) associated with outcomes quantifies the uncertainty about the event.

• True
• False

Q4. For the continuous case, the probability associated with any particular point is zero

• True
• False

Q5. The variance of a random variable may be either positive or negative.

• True
• False

#### Quiz 1: End of Week

Q1. A hypothesis is a claim (assumption) about a population parameter, but sometimes about a sample statistic.

• True
• False

Q2. If we reject a true null hypothesis, we commit a Type I Error.

• True
• False

Q3. A two-tailed test involves both negative and positive values.

• True
• False

Q4. The null hypothesis always contains “=” , “\le≤” or “\ge≥” sign.

• True
• False

#### Quiz 2: End of Course Quiz

Q1. Which of the following is true of the null and alternative hypotheses?

• Exactly one hypothesis must be true
• Both hypotheses must be true
• It is possible for neither hypothesis to be true

Q2. The ratio between the two variances…

• Gives us the measure of the relative efficiency of \hat{\beta}_1β^​1​ with respect to \hat{\beta}_2β^​2​
• Gives us the correlation coefficient between variables
• Gives a measure of unbiasedness

Q3. Which of the following statements is true for “outliers”?

• They should be deleted from the analysis
• They can distort summary statistics
• They are mistakes made in the analysis

Q4. A type II error occurs when…

• the null hypothesis is incorrectly accepted when it is false
• the null hypothesis is incorrectly rejected when it is true
• the sample mean differs from the population mean

Q5. Given the following set of data, what is the range?

• 12 23 34 54 21 8 9 67
• 59
• 28.5
• 8

Q6. A one-tailed test…

• requires more evidence to reject the null hypothesis
• requires less evidence to reject the null hypothesis
• a one-tailed test cannot be performed

Q7. The t statistic is…

• the critical value
• the mean of a random variable
• a function of a random sample

Q8. Which of the following sentences best describes random sampling?

• Random sampling is the complete set of all items that interest an investigator
• Random sampling is an observed subject (or portion) of a population
• Random sampling means that every possible sample of a given size, nn, has the same chance of selection- that is j=N/nj=N/n.

Q9. If we want to draw attention to the proportion of frequencies in each category of variables

• We use a pie chart
• We use a line chart
• We use bar chart

Q10. If data is skewed to the right, the measure of skewness will be…

• Negative
• Neutral
• Positive

Q11. Which of the following is true?

• Categorical variables produce responses that belong to groups of categories
• Categorical variables are quantitative variables
• Categorical variables usually arise from a counting process

Q12. Focusing on describing or explaining data versus going beyond immediate data and making inferences is the difference between…

• Central tendency and common tendency
• Mutually exclusive and mutually exhaustive properties
• Descriptive and inferential

Q13. If a distribution is skewed to the left, then it is:

• Negatively skewed
• Positively skewed
• Symmetrically skewed

Q14. If Cov(x,y)<0Cov(x,y)<0 then…

• xx and yy tend to move in opposite directions
• xx and yy tend to move in the same direction
• There is no covariance.

Q15. One-tailed alternatives are phrased in terms of

• \neq​=
• \gt> or \lt<
• \le≤ or \ge≥

Q16. If the data is severely skewed, what is the preferred measure of central tendency?

• Mean
• Median
• Mode

Q17. The value set for \alphaα is known as…

• the rejection level
• the acceptance level
• the significance level

Q18. Which of the following statements is false?

• The covariance is the only numerical way to describe a linear
relationship between variables
• The covariance measures the direction of a linear relationship between two variables
• The correlation coefficient ranges between –1 and 1

Q19. Measures of central tendency are:

• Inferential statistics that identify the best single value for representing a set of data
• Descriptive statistics that identify the best single value for representing a set of data
• Inferential statistics that identify the spread of the score in a data set

Q20. If Cov(x,y)=0Cov(x,y)=0, then…

• xx and yy tend to move in the same direction
• xx and yy tend to move in opposite directions
• xx and yy are independent

Q21. A restriction is…

• a method which minimizes the residual sum of squares
• the null hypothesis
• the alternative hypothesis

Q22. The regression analysis…

• is a measure of the degree of linear association between variables
• treats the variables in exactly the same way
• aims at finding the model which best fits the data

Q23. Given the model y_t=\alpha+\beta{x_t}+u_ty

• We need to find \alphaα and \betaβ, which minimize the vertical distance between the estimate line and the data
• We need to find \alphaα and \betaβ, which describe any kind of relationship between xx and yy
• We need to find \alphaα and \betaβ, which must be positive

Q24. An estimator is unbiased if…

• the difference between the mean value and the true value E[\hat\beta]-\betaE[β^​]−β is equal to 0
• a particular value \hat\betaβ^​ is equal to the correct value of \betaβ
• it has the minimum variance among all the other estimators with the same statistical properties

Q25. Which of the following is not a measure of central tendency?

• Median
• Mean
• Covariance

Q26. What is the first stage of statistics?

• Organizing data
• Collecting data
• Summarizing data

Q27. Which of the following is used to represent a known value of the population variance?

• S
• \sigmaσ
• \sigma^2σ2

Q28. A parameter is…

• a numerical measure that describes a specific characteristic of a sample
• a numerical measure that describes a specific characteristic of a population
• a statistic computed from a sample that gives a single value for the unknown parameter, \betaβ