Q: A company’s quarterly revenue by category is: Electronics: $$180,000; Clothing: 140$$,000; Groceries: $$120,000; Other: 110$$,000. What percentage of total revenue is contributed by Clothing?

$$ \frac{140}{550} \times 100 = 25.45\% $$

Q: Using the regression equation $$ \hat{y} = 5.233x + 29.274 $$, what is the predicted monthly revenue if advertising spending is $42,000?

$$ \hat{y} = 5.233 \times 4.2 + 29.274 = 51.2576 (i.e$$., $512,576)

Question 1

A data analyst is studying monthly profit (in dollars), region (East, Midwest, West), customer complaint rate (percentage), and manager experience level (Entry, Intermediate, Senior, Executive) for a national restaurant chain. In this context, who is the 'WHO' and what are the types of the variables (categorical or quantitative)?

Accepted Answer

The 'WHO' is the restaurant locations; monthly profit and customer complaint rate are quantitative, region and manager experience level are categorical.

Question 2

A movie theatre collects data on movie genre, customer age, ticket price, ticket type, and showtime category. Which graph is most appropriate for displaying the distribution of customer age?

Accepted Answer

Histogram

Question 3

A retail store records the following spending amounts (in dollars) during a weekend sale: 10, 18.75, 20, 15.90, 19.80, 19.60, 24.30, 14.25, 27.80, 31.50, 10.40, 16.85, 21.70, 30, 38.60. If you construct a histogram with bins of width 5 starting at [10,15], how many data points fall into the [15,20) bin?

Accepted Answer

4

Question 4

A company’s quarterly revenue by category is: Electronics: $$180,000; Clothing: 140$$,000; Groceries: $$120,000; Other: 110$$,000. What percentage of total revenue is contributed by Clothing?

Accepted Answer

$$ \frac{140}{550} 	imes 100 = 25.45\% $$

Question 5

Given the monthly sales (in thousands): 50, 76, 42, 69, 52, 47, 49, 120, 53, 51, what is the five-number summary?

Accepted Answer

Min: 42, Q1: 49, Median: 51.5, Q3: 69, Max: 120

Question 6

A manufacturing company records production hours and product defects for 9 observations. The scatter plot shows that as production hours increase, product defects tend to increase as well. How would you describe the direction, form, and strength of the relationship?

Accepted Answer

Positive direction, linear form, moderate strength

Question 7

The annual incomes (in $10,000s) of 6 employees are: 38, 51, 46, 79, 57, 83. What is the mean income?

Accepted Answer

$$ \frac{38+51+46+79+57+83}{6} = 59.0 $$

Question 8

Two stores, Maple Mart and Harbour Shop, each have an average daily sale of $1200 over five days. Maple Mart’s sales are: 1180, 1210, 1190, 1205, 1215. Harbour Shop’s sales are: 900, 1500, 700, 1800, 1100. Which store has more consistent sales, and why?

Accepted Answer

Maple Mart, because it has a lower standard deviation

Question 9

A music shop’s regression line for predicting monthly revenue ($$10,000s) from advertising spending (10$$,000s) is $$ \hat{y} = 5.233x + 29.274 . $$What does the slope mean in this context?

Accepted Answer

For each additional $$10,000 spent on advertising, monthly revenue is predicted to increase by 52$$,330.

Question 10

Using the regression equation $$ \hat{y} = 5.233x + 29.274 $$, what is the predicted monthly revenue if advertising spending is $42,000?

Accepted Answer

$$ \hat{y} = 5.233 	imes 4.2 + 29.274 = 51.2576  (i.e$$., $512,576)

Question 11

A company’s HR department finds that 42 out of 153 employees prefer remote work. What is the probability that a randomly selected employee prefers remote work?

Accepted Answer

$$ \frac{42}{153} \approx 0.2745 $$

Question 12

In the same HR study, what is the probability that a randomly selected employee works in the Accounting department and prefers on-site work?

Accepted Answer

$$ \frac{18}{153} \approx 0.1176 $$

Question 13

A store has 7 customers during a flash promotion. Each customer independently makes a purchase with probability 0.60. What is the expected number of purchases?

Accepted Answer

$$ E(X) = np = 7 	imes 0.6 = 4.2 $$

Question 14

For the same store, what is the variance of the number of purchases?

Accepted Answer

$$ V(X) = npq = 7 	imes 0.6 	imes 0.4 = 1.68 $$

Question 15

A national retailer finds that 14% of employees participate in a program. In a random sample of 400 employees, what is the mean and standard deviation of the number of participants?

Accepted Answer

Mean: $$ \mu = np = 400 	imes 0.14 = 56 $$; SD: $$ \sigma = \sqrt{400 	imes 0.14 	imes 0.86} \approx 6.93 $$

Question 16

A financial advisor claims 20% of clients experience positive returns. In a sample of 250 clients, what is the probability that between 18% and 25% of the sample experience positive returns? (Use normal approximation.)

Accepted Answer

First, calculate mean $$ \mu = np = 250 	imes 0.2 = 50 $$, SD $$ \sigma = \sqrt{250 	imes 0.2 	imes 0.8} = 6.32 . $$For 18%: $$ x_1 = 0.18 	imes 250 = 45 $$; for 25%: $$ x_2 = 0.25 	imes 250 = 62.5 . $$Find $$ P(45 \u003c X \u003c 62.5) $$ using normal approximation.

Question 17

A company finds that 160 out of 200 employees did not click on phishing links after training. Construct a 95% confidence interval for the true proportion of all trained employees who would avoid clicking phishing links.

Accepted Answer

Sample proportion $$ \hat{p} = \frac{160}{200} = 0.8 . 95$$% CI: $$ 0.8 \pm 1.96 	imes \sqrt{\frac{0.8 	imes 0.2}{200}} = 0.8 \pm 0.0557 $$, so (0.744, 0.856).

Question 18

A retailer wants to estimate the proportion of satisfied customers to within 5% with 90% confidence. If 75% of customers are estimated to be satisfied, what is the minimum sample size required?

Accepted Answer

$$ n = \left( \frac{z^*}{E} ight)^2 \hat{p}(1-\hat{p}) = \left( \frac{1.645}{0.05} ight)^2 	imes 0.75 	imes 0.25 \approx 203 $$

Question 19

A retail chain samples 200 Nike customers (150 returns) and 180 Adidas customers (120 returns). Construct a 99% confidence interval for the difference in return rates (Nike - Adidas).

Accepted Answer

Nike: $$ \hat{p}_1 = 0.75 $$, Adidas: $$ \hat{p}_2 = 0.6667 . SE$$: $$ \sqrt{\frac{0.75 	imes 0.25}{200} + \frac{0.6667 	imes 0.3333}{180}} \approx 0.048 $$; CI: $$ 0.75 - 0.6667 \pm 2.576 	imes 0.048 = 0.0833 \pm 0.124 $$, so (-0.041, 0.207).

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