Q: Given the 'Employee Salary Analysis' dataset, the multiple regression equation for predicting salary (Y, in $$1000s) based on experience (X_1$, in years) and gender (X_2$, 0 = female, 1 = male) is Y = 29.17 + 4.17X_1 + 3.33X_2$. What is the predicted salary for a male employee with 10 years of experience?

$$Y = 29.17 + 4.17 \times 10 + 3.33 \times 1 = 73.2$$

Q: A cafe analyzed whether customers tipped based on their payment method. What is the probability that a customer did not tip, given that the customer paid by card?

$$P(\text{Did Not Tip} | \text{Paid by Card}) = \frac{42}{18+42} = 0.70$$

Q: A student is chosen at random from all secondary school students in Illinois and Florida. What is the probability that the student is enrolled in Florida, given that the student is in the 11th grade?

$$P(\text{Florida} | \text{11th Grade}) = \frac{370}{416} \approx 0.89$$

Question 1

Given the 'Employee Salary Analysis' dataset, the multiple regression equation for predicting salary (Y, in $$1000s) based on experience (X_1$, in years) and gender (X_2$, 0 = female, 1 = male) is Y = 29.17 + 4.17X_1 + 3.33X_2$. What is the predicted salary for a male employee with 10 years of experience?

Accepted Answer

$$Y = 29.17 + 4.17 	imes 10 + 3.33 	imes 1 = 73.2$$

Question 2

Based on the regression equation $$Y = 29.17 + 4.17X_1 + 3.33X_2$$, does gender have a significant effect on salary?

Accepted Answer

Yes, because the coefficient for gender ($$3.33) is $$not zero, indicating a difference in salary between genders.

Question 3

Which sampling method is used when a student stands outside the cafeteria at lunchtime and interviews students who are leaving, and what is a potential source of bias?

Accepted Answer

Convenience sampling; non-representative sample bias

Question 4

You have the following frequency distribution for delivery times (in minutes): 10–19: 4, 20–29: 7, 30–39: 12, 40–49: 8, 50–59: 3. Which histogram best represents this data?

Accepted Answer

The histogram with a peak at 34.5 and frequencies matching 4, 7, 12, 8, 3 (Image 3)

Question 5

If a frequency polygon has class midpoints labeled as 20, 40, 60, and 80, what does a point at $$x=60$$ and $$y=20$$ represent?

Accepted Answer

The class with midpoint 60 has a frequency of 20.

Question 6

Given the dataset [1, 2, 2, 4, 4, 4, 5], how many dots will be stacked above the number 4 in the dot plot?

Accepted Answer

Three dots

Question 7

A city council is analyzing water usage fees in four neighborhoods. The boxplot shows North has a higher median than the other neighborhoods. What conclusion can be drawn?

Accepted Answer

Yes, North has the highest median

Question 8

A cafe analyzed whether customers tipped based on their payment method. What is the probability that a customer did not tip, given that the customer paid by card?

Accepted Answer

$$P(	ext{Did Not Tip} | 	ext{Paid by Card}) = \frac{42}{18+42} = 0.70$$

Question 9

A consumer feedback agency surveyed 1,115 shoppers. The Pareto chart shows 345 believe the policy is 'Extremely Unfair.' What is the probability of selecting a shopper who believes the policy is extremely unfair?

Accepted Answer

$$P = \frac{345}{1115} \approx 0.31$$

Question 10

A student is chosen at random from all secondary school students in Illinois and Florida. What is the probability that the student is enrolled in Florida, given that the student is in the 11th grade?

Accepted Answer

$$P(	ext{Florida} | 	ext{11th Grade}) = \frac{370}{416} \approx 0.89$$

Question 11

In the context of data collection, which of the following best describes a census?

Accepted Answer

A census collects data from every individual in the population

Question 12

If the probability that an event $$E$$ will not occur is $$P(\overline{E}) = 0.86$$, what is the probability that the event will occur?

Accepted Answer

$$P(E) = 1 - 0.86 = 0.14$$

Question 13

A computer program randomly generates a digit from 0 to 9. What is the sample space and how many possible outcomes are there?

Accepted Answer

Sample space: $$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$; Number of possible outcomes: $$10$$

Question 14

A rare genetic disorder affects 1 out of every 500 individuals. A screening test returns a positive result 90% of the time when a person actually has the disorder, and 4% of the time when a person does not have the disorder. If a person tests negative, what is the probability that they do not have the disorder? (Use Bayes' Theorem.)

Accepted Answer

$$P(	ext{No Disorder} | 	ext{Negative}) \approx 0.9998$$

Question 15

If you have 2 types of bread, 3 types of meat, and 4 types of cheese, how many different sandwiches can you make (choosing one of each)?

Accepted Answer

$$2 	imes 3 	imes 4 = 24$$

Question 16

A security badge code is made up of 5 characters. Each character can be any uppercase letter (A–Z) or digit (0–9), except the first character must be a letter and the last character must be an even digit. What is the probability of guessing the correct badge code on the first attempt?

Accepted Answer

$$\frac{1}{1,679,616}$$

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