Question

Based on the respondents location in the north or south of the state the table shows survey results regarding their preferred fruit grapes or cherries
Cherries. Grapes
North. 120. 125
South. 25. 75

Examine the data from a survey about the part of the state people are from and the fruit they prefer using relative frequencies is the following statement true or false people from the north tend to like cherries more than grapes

Answer 1

To determine whether people from the North tend to like cherries more than grapes based on the survey data, we can calculate the relative frequencies for both fruits for respondents from the North.

Here's the data we have:

- North: 120 (Cherries), 125 (Grapes)
- South: 25 (Cherries), 75 (Grapes)

First, let's find the total number of respondents from the North:

\[
\text{Total North} = 120 + 125 = 245
\]

Now, we can calculate the relative frequencies for each fruit among respondents from the North:

\[
\text{Relative frequency of Cherries (North)} = \frac{120}{245} \approx 0.4898 \quad \text{(or 48.98\%)}
\]

\[
\text{Relative frequency of Grapes (North)} = \frac{125}{245} \approx 0.5102 \quad \text{(or 51.02\%)}
\]

Comparing the relative frequencies:

- Cherries: approximately 48.98%
- Grapes: approximately 51.02%

Since the relative frequency of grapes (51.02%) is greater than that of cherries (48.98%) for respondents from the North, the statement "people from the North tend to like cherries more than grapes" is **false**.