Question

construct and interpret two-way frequency tables

1. attend to precision in a survey of 200 people who visited china, 85% visited the great wall. of those who visited the great wall, 30% also visited the chengdu panda center. of those who did not visit the great wall, 80% visited the panda center.

complete the two-way frequency table.

visited great wall

did not visit great wall

total

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visited chengdu panda center

did not visit chengdu panda center

total

200

2. math on the spot determine whether there is an association between the events.

a. thirty-two students were polled about whether they have a phone plan with texting and whether they have had an accident. find the percentages of those having an accident for both the general population of students and for students who have a phone with texting. is there an association between having a phone with texting and having an accident?

	accident	no accident	total		---	---	---	---		phone plan with texting	12	8	20		phone plan without texting	4	8	12		total	16	16	32	b. middle school and high school students were polled about whether they had visited an amusement park. find the percentages of those having visited an amusement park for both the general population of students and for high school students. is there an association between being a high school student and visiting an amusement park?
	visited	did not visit	total		---	---	---	---		middle school student	20	5	25		high school student	60	15	75		total	80	20	100

Explanation:

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Problem 1: Complete the two-way table

Step1: Calculate Great Wall visitors

Total people = 200. 85% visited Great Wall:
$200 \times 0.85 = 170$
People who did not visit Great Wall:
$200 - 170 = 30$

Step2: Panda Center visitors (Great Wall group)

30% of 170 visited Panda Center:
$170 \times 0.30 = 51$
Great Wall visitors who did not visit Panda Center:
$170 - 51 = 119$

Step3: Panda Center visitors (non-Great Wall group)

80% of 30 visited Panda Center:
$30 \times 0.80 = 24$
Non-Great Wall visitors who did not visit Panda Center:
$30 - 24 = 6$

Step4: Calculate row totals

Total Panda Center visitors:
$51 + 24 = 75$
Total non-Panda Center visitors:
$119 + 6 = 125$
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Problem 2A: Analyze association for texting/accidents

Step1: General accident percentage

Total accidents = 16, total students = 32:
$\frac{16}{32} \times 100 = 50\%$

Step2: Texting plan accident percentage

Accidents with texting = 12, texting students = 20:
$\frac{12}{20} \times 100 = 60\%$

Step3: Compare percentages

60% ≠ 50%, so association exists.
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Problem 2B: Analyze association for school/amusement park

Step1: General visited percentage

Total visited = 80, total students = 100:
$\frac{80}{100} \times 100 = 80\%$

Step2: High school visited percentage

High school visited = 60, high school students = 75:
$\frac{60}{75} \times 100 = 80\%$

Step3: Compare percentages

80% = 80%, so no association exists.

Answer:

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Completed Two-Way Table (Problem 1):

	Visited Great Wall	Did not visit Great Wall	TOTAL
Did not visit Chengdu Panda Center	119	6	125
TOTAL	170	30	200

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Problem 2A:

• General student accident rate: 50%
• Students with texting plan accident rate: 60%
• Answer: Yes, there is an association between having a phone plan with texting and having an accident, as the accident rate is higher for students with a texting plan.

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Problem 2B:

• General student amusement park visit rate: 80%
• High school student amusement park visit rate: 80%
• Answer: No, there is no association between being a high school student and visiting an amusement park, as the visit rate matches the general student population.