Question

students at a japanese immersion school must study one of the traditional art forms of japan. a random sample of 50 students from the school are asked which traditional art form they study. the results of the survey are shown in the table. determine if each inference is valid or not valid. (when an inference is valid, the statement is reasonable or correct based on the given information.) about 40% of students at the school study flower arranging. approximately 14 students at the school study the tea ceremony. in a group of 200 students at the school, about 28 of the students study the drums.

Explanation:

Step1: Calculate the percentage for flower arranging

The formula for percentage is \(\frac{\text{frequency}}{\text{total sample}}\times100\).
For flower arranging, frequency \(f = 12\), total sample \(n=50\).
\(\frac{12}{50}\times100=\frac{12\times100}{50}=24\%
eq40\%\)

Step2: Analyze the statement about tea - ceremony

The sample is of 50 students. Saying approximately 14 students study tea - ceremony (where in the sample of 50, 14 study tea - ceremony) is a wrong generalization. We can't say for the whole school (unknown size) that exactly 14 study tea - ceremony.

Step3: Calculate the number of drum - studying students in a group of 200

The proportion of drum - studying students in the sample is \(\frac{7}{50}\).
For a group of \(N = 200\) students, the number of drum - studying students is \(x=\frac{7}{50}\times200=\frac{7\times200}{50}=28\)

Answer:

1. Not Valid
2. Not Valid
3. Valid