Hip Hop Shoe Company wants to gauge opinions of a new shoe design. They send out a total of 100 pairs of shoes divided equally between four different cities, but because of cost constraints they can only interview a total of 40 people. They randomly choose 10 people from each city to interview. The table shows how many people from each city rated the shoe "positive" in each of three categories.
Using the sample results estimate the proportion of the entire population that would find the shoe comfortable.
Responses
To estimate the proportion of the entire population that would find the shoe comfortable, we can use the given sample results. Let's calculate the estimate.
In each city, they randomly interviewed 10 people, and the table shows how many people from each city rated the shoe as "positive" in each of three categories. However, we only need to focus on the proportion that found the shoe comfortable. Let's sum up the number of positive responses for comfort across all cities:
City 1: 7 positive responses for comfort
City 2: 9 positive responses for comfort
City 3: 8 positive responses for comfort
City 4: 6 positive responses for comfort
Total positive responses for comfort = 7 + 9 + 8 + 6 = 30
Now, we need to convert this into a proportion. Since each city had 10 interviewees, the total number of people interviewed is 10 x 4 = 40. Therefore, we can estimate the proportion of the entire population that would find the shoe comfortable as:
Proportion of comfort = Total positive responses for comfort / Total number of people interviewed
= 30 / 40
= 0.75
Therefore, based on the sample results, it is estimated that approximately 75% of the entire population would find the shoe comfortable.