A researcher is examining the relationship between color preference and gender. A sample of 30 men and 30 women is obtained and each person is asked to identify his/her preference between two choices of paint colors for a new student lunge. For this sample,
5 of the men preferred color A, and 15 of the women preferred color A. If a χ2- test is used to evaluate the relationship, what is the expected frequency for men preferring color A?
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30/15=2 30/5=6 6+2=12
answer: 12
To determine the expected frequency for men preferring color A, we need to use the chi-squared test. This test is used to analyze categorical data and determine if there is a statistically significant relationship between two variables.
To calculate the expected frequency, we need to use the formula:
Expected Frequency = (row total * column total) / grand total
In this case, we want to find the expected frequency for men preferring color A. Let's break down the given information:
- There are 30 men and 30 women in the sample.
- 5 out of the 30 men preferred color A.
- 15 out of the 30 women preferred color A.
We can set up a contingency table to summarize the data:
Color A Color B Total
Men 5 ? 30
Women 15 ? 30
Total 20 ? 60
The total number of people who preferred color A is 5 (men) + 15 (women) = 20.
Using the formula, we can calculate the expected frequency for men preferring color A:
Expected Frequency for men preferring color A = (30 * 20) / 60 = 10.
Therefore, the expected frequency for men preferring color A is 10.