Practice Quiz Answers

AP Stats

162 Points Name______Key______

A recent survey in California asked people whether they lived in an urban, suburban, or rural area. It also asked the participants to rate the importance of planting trees in urban areas. The results are in the following table.

Important / Slightly
Important / Not Important
At All / Total
Urban / 432 / 213 / 198 / 843
Suburban / 277 / 124 / 67 / 468
Rural / 97 / 117 / 265 / 479
Total / 806 / 454 / 530 / 1790

A person is randomly selected from the respondents to the survey. Find the probability

1.  that the person is from an urban area. .4709

2.  that the person believes the planting of trees in urban areas is important.

.4503

3.  that the person is not from a rural area.

.7324

4.  that the person is from an urban area or from a rural area.

.7385

5.  that the person is from an urban area if it is known that the person believes that the planting of trees in urban areas is important.

.536

6.  that the person is from an urban area and believes that the planting of trees in urban areas is important.

.2413

7. Are the events slightly important and rural independent? Show all work and explain.

NO9* Check your notes

8 What will you do once you graduate? Where will you live? A report in American Demographics indicates that 60% of all college students plan to move back home after graduation. A group of 80 college students are randomly selected and asked whether or not they plan to move back home after graduation.

a.  What is the probability that between 47 and 66 of the students plan to move back home?

.6364

b.  What is the probability that fewer than 51 of the students plan to move back home?

.7139

c.  What is the probability that exactly 49 of the students plan to move back home?

.0889

9. A police chief in Bridgeville claims 70 % of the drivers on Aton Street are speeding. A random sample of 250 drivers showed 146 speeders. Use a confidence interval to test the chief’s estimate. Explain your conclusions. (.5229, .6451) Since the chief’s claim is not in the interval, it is unlikely that 70% of the drivers on Aton Street are speeding.

10. A variable with a Poisson distribution has a mean of 225. Use the empirical rule to find an interval where 99.7% of the values should occur. What proportion of the values are in the interval?

SKIP

For each following problem, state the null and alternative hypothesis, the critical z value, α, your assumptions, the test statistic and p value. Show the proper formula, and the formula filled in with the values in the problem. Write a conclusion based on your results. Problems like this are 30-40 points.

11. Commercials in Space. The commercialism of our space program was the topic of Exercise 8.16. In a survey of 500 men and 500 women, 20% of the men and 26% of the women responded that space should remain commercial-free. Is there a significant difference in the population proportions of men and women who think that space should remain commercial-free? Use α = 0.01.

Items in red are optional; all text in black is part of a complete solution!

We are testing to see if the proportions of men and women are equal.

Assumptions: Sample is very large, we can assume a random sample

all are over 5

Two proportion z test

Critical z value is

P=.0242

Fail to reject , there is insufficient evidence to conclude the proportion of men and women who think space should remain commercial free is different.

12. A study was conducted to compare the mean number of emergency calls in two different zones in the city. Samples of 100 eight hour shifts were randomly selected for each of the two regions, and the number of emergency calls was logged for each shift. The sample statistics are listed below. Test to see if the regions are different at the level Explain your results.

Region 1 / Region 2
Sample mean / 3.4 / 4.0
Sample variance / 2.96 / 2.52

We are testing to see if the mean number of emergency calls between the two regions is different.

Let represent region1 and represent region 2

Assumptions: random sample, , both 30

2 sample z test

Critical z value is ≠2.58

Fail to reject the null; there is insufficient evidence to suggest the regions receive a different amount of emergency calls

13. Researchers at a large university wished to test a research hypothesis suggesting women were more likely than men to be chocolate lovers. Testing of 456 randomly selected women resulted in 75% being chocolate lovers. 350 randomly selected men were also tested with 82% being identified as chocolate lovers. Is there evidence to suggest women are more likely to be chocolate lovers than men? Explain.

Try this problem, show me the work and check my answer key in class

14. A certain brand of car is rated to get 30 miles per gallon on the highway. A researcher believes the claim is faulty – that it is too high. His company drives a random sample of 35 cars in identical highway conditions for a total of 500 miles and checks the fuel economy. He finds that the average rating for the cars is 29.52 miles per gallon. Using a population standard deviation of 1.1 mpg, determine if there is evidence at the 2% level that the company’s claim of 30 mpg is too high. Also, find a 98% confidence interval for the average mileage rating of the car and interpret the interval.

Try this problem, show me the work and check my answer key in class