Question

At a local bar in a small Midwestern town, beer and wine are the only two alcoholic options. The manager noted that of all male customers who visited over the weekend, 152 ordered beer, 42 ordered wine, and 29 asked for soft drinks. Of female customers, 34 ordered beer, 17 ordered wine, and 13 asked for soft drinks. a. Construct Contingency table that shows frequencies for the qualitative variables Gender (male or female) and Drink Choice (beer, wine, or soft drink). 152 42 29 34 17 13 186 59 42 b. Find the probability that a customer orders wine. (Round your intermediate calculations and final answer to 4 decimal places.) 0.2056 c. What is the probability that a male customer orders wine? (Round your intermediate calculations and final answer to 4 decimal places.) 0.1883 d. Are the events "Wine" and "Male" independent? No because P("Wine" | "Male") ≠ P("Wine").

Answer 1

To construct a contingency table, we create a table with two rows and three columns representing the genders and drink choices, respectively. We then fill in the frequencies based on the given data.

Step-by-step explanation:

To construct a contingency table for the given data, we will create a table with two rows representing the genders (male and female) and three columns representing the drink choices (beer, wine, and soft drink). We will then fill in the frequencies in each cell based on the given information.

Males: 152 ordered beer, 42 ordered wine, and 29 asked for soft drinks.

Females: 34 ordered beer, 17 ordered wine, and 13 asked for soft drinks.

BeerWineSoft DrinkMale1524229Female341713
a. Contingency table:

Beer

Wine

Soft Drink

Male

152

42

29

Female

34

17

13

Total

186

59

42

Male

Female

Total

​

Beer

152

34

186

​

Wine

42

17

59

​

Soft Drink

29

13

42

​

​

b. Probability that a customer orders wine:

�

(

Wine

)

=

Number of customers ordering wine

Total number of customers

=

59

287

≈

0.2056

P(Wine)=

Total number of customers

Number of customers ordering wine

​

=

287

59

​

≈0.2056

c. Probability that a male customer orders wine:

�

(

Wine | Male

)

=

Number of male customers ordering wine

Total number of male customers

=

42

223

≈

0.1883

P(Wine | Male)=

Total number of male customers

Number of male customers ordering wine

​

=

223

42

​

≈0.1883

d. To check for independence, we compare

�

(

Wine | Male

)

P(Wine | Male) with

�

(

Wine

)

P(Wine).

If the events are independent, then

�

(

Wine | Male

)

P(Wine | Male) should be equal to

�

(

Wine

)

P(Wine). In this case,

0.1883

0.1883 is not equal to

0.2056

0.2056, so the events "Wine" and "Male" are not independent.

Answer 2

A contingency table segregates frequencies of gender and drink choice into a matrix, which facilitates the calculation of probabilities regarding wine orders and tests the independence of gender and drink choice as events.

Step-by-step explanation:

Constructing a Contingency Table

To construct a contingency table for the frequencies of gender and drink choice, we use the numbers provided to fill in the categories. A contingency table will have the drink choices as columns and gender as rows. Each cell in the table represents the frequency for the corresponding combination of row (gender) and column (drink choice).

Here is one way the table might look:

Beer
Wine
Soft Drink


Male
152
42
29


Female
34
17
13

Calculating Probabilities

To calculate the probability that a customer orders wine, we add the number of males who ordered wine to the number of females who ordered wine and divide by the total number of customers. To find the probability that a male customer orders wine, divide the number of males who ordered wine by the total number of male customers

Independence of Events

To determine if the events "Wine" and "Male" are independent, we compare the overall probability of ordering wine with the conditional probability of a male ordering wine. If these probabilities are the same, the events are independent; if not, they are dependent.