Practice Test
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Start by constructing an empty table with the appropriate column and row headers. Then, use the given information to find the missing frequencies.
Table:
| Uses Reusable Bags | |||
|---|---|---|---|
| Gender | Yes | No | Total |
| Females | 60 | 50 | 110 |
| Males | 15 | 45 | 60 |
| Total | 75 | 95 | 170 |
Probability: 1/4
A two-way table is a frequency table that displays data collected from one source that belongs to two different categories. One category of data is represented by rows and the other is represented by columns. We want to organize the given information in a two-way table. To do so, we will follow three steps.
Let's do these three things one at a time. Then, we will estimate the probability that a randomly selected male shopper uses reusable bags.
| Uses Reusable Bags | |||
|---|---|---|---|
| Gender | Yes | No | Total |
| Female | |||
| Male | |||
| Total | |||
Each entry in the table is called a joint frequency. We are told that of the 60 males surveyed, 15 use reusable bags. Of the 110 females surveyed, 60 use reusable bags. With this information, we can find the numbers of men and women that do not use reusable bags. Males using reusable bags:& 60- 15= 45 Females using reusable bags:& 110- 60= 50 Let's use this information to start filling in our table.
| Uses Reusable Bags | |||
|---|---|---|---|
| Gender | Yes | No | Total |
| Females | 60 | 50 | 110 |
| Males | 15 | 45 | 60 |
| Total | |||
The sums of the rows and columns are called marginal frequencies. Let's calculate these sums to find the missing marginal frequencies. Shoppers using a reusable bag:& 60+ 15=75 Shoppers not using a reusable bag:& 50+ 45=95 Finally, we have two ways of calculating the grand total. We can add the total number of females surveyed to the total number of males surveyed, or we can add the total number of shoppers using reusable bags to the total number of shoppers not using reusable bags. These two numbers must be the same! Grand total l 110+ 60 =170 75 + 95=170 ✓ Finally, we can complete our table!
| Using a Reusable Bags | |||
|---|---|---|---|
| Gender | Yes | No | Total |
| Females | 60 | 50 | 110 |
| Males | 15 | 45 | 60 |
| Total | 75 | 95 | 170 |
Using the data from the survey, we will estimate the probability that a randomly selected male shopper uses reusable bags. We will do this by dividing the number of male shoppers who use reusable bags by the number of male shoppers who were surveyed. 15/60 ⇔ 1/4 The probability that a randomly selected male shopper uses reusable bags is 14, or 0.25.