Chapter 8 Quiz 1 - d2ct263enury6r.cloudfront.net

1 Statistics in Action Instructor s Resource Book Chapter 8 quiz 1 1 2008 Key Curriculum Press Chapter 8 quiz 1 Name _____ Date _____ 1. Use this completed chart of reasonably likely outcomes to answer these questions. a. According to a recent report, about 45% of 20- and 21-year-olds are enrolled in school. How many enrolled students is it reasonably likely to get in a sample of 40 randomly chosen 20- and 21-year-olds? b. Suppose that in a random sample of 40 adults, 12 of the adults have never married. Find the 95% confidence interval for the proportion of all adults who have never married.

2 2. A recent survey of 800 randomly selected households in the United States found that approximately of the households have Internet access. a. Check whether the three conditions for computing a confidence interval are met in this case. b. Regardless of your answer to part a, compute the 95% confidence interval for the proportion of households in the United States that have Internet access. What is the margin of error? c. What is it that you are 95% sure is in the confidence interval? d. Interpret this confidence interval. e. Explain the meaning of 95% confidence.

3 3. According to a recent report, about 70% of all households have cable television. You think this proportion has changed and decide to test it. You take a random sample of 40 households and find that only 24 of the households have cable television. a. What is the standard p0? b. What is the alternative hypothesis? c. What is the sample proportion p? d. Using the chart given in Question 1, is the result statistically significant? 4. Assume your null hypothesis is that of all households currently have Internet access. You take a random sample of 50 households and find that 34 of the households have Internet access.

4 Find the test statistic for this situation, and give your conclusion if a= Statistics in Action Instructor s Resource Book Chapter 8 quiz 2 1 2008 Key Curriculum Press Chapter 8 quiz 2 Name _____ Date _____ 1. Use Table A, Standard Normal Probabilities, or a calculator to answer these questions for a two-sided test. a. What critical value is associated with a level of significance of b. What level of significance is associated with critical values of * ? 2. Suppose that in a random sample of 500 households, you find that 309 households have a computer.

5 Follow the steps given in parts a d to test the claim that of all households in the United States have a computer. Use a significance level of a. Name the test and check the conditions needed for it. b. State the hypotheses in words and symbols. c. Calculate the value of the test statistic and draw a sketch. d. Calculate the P-value for the test. Use this P-value in a sentence that explains what it represents. e. What is your conclusion? Explain in the context of this problem. 3. Consider again the situation in Question 2. Suppose the null hypothesis were instead that or fewer of all households in the United States have a computer.

6 A. State the new alternative hypothesis in words and symbols. b. Calculate the new P-value for the test. Use this P-value in a sentence that explains what it represents. c. Does your conclusion change? Explain in the context of this problem. 4. Ean is spinning a particular penny to test whether spinning this penny results in heads 40% of the time against the alternative that the percentage of heads differs from 40%. She doesn t know it, but this particular penny actually results in heads 25% of the time. She will use a significance level of Ean spins this penny 100 times and gets heads 32 times.

7 A. What conclusion should Ean come to? b. Did Ean make an error? If so, which type? Statistics in Action Instructor s Resource Book Chapter 8 quiz 3 1 2008 Key Curriculum Press Chapter 8 quiz 3 Name _____ Date _____ 1. The UCLA Center for Communication Policy found that of Americans used the Internet in 2001 and used the Internet in 2002. You want to estimate the change in the proportion of all Americans who used the Internet in these two years. Assume that the samples were independently and randomly selected and that the sample size was 1006 in both years.

8 A. Check whether the three conditions for computing a confidence interval are met in this case. b. Regardless of your answer to part a, compute the 95% confidence interval for this situation. c. Interpret this confidence interval. Make it exactly clear as to what it is that you are 95% sure is in the confidence interval. 2. Linus Pauling believed that vitamin C prevents colds and conducted a now-famous medical experiment to prove his theory. His subjects were 279 French skiers who were randomly assigned to receive either vitamin C or a placebo. Of the 139 given vitamin C, 17 got a cold.

9 Of the 140 given the placebo, 31 got a cold. Using a one-sided test, find out if these data support the conclusion that vitamin C prevents colds. Use a significance level of a. Name the test and check the conditions needed for it. b. State the hypotheses. c. Calculate the value of the test statistic and draw a sketch. d. Calculate the P-value for the test. e. What is your conclusion? Explain in the context of this problem. Statistics in Action Instructor s Resource Book Chapter 8 Test A 1 2008 Key Curriculum Press Chapter 8 Test A Name _____ Date _____ 1.

10 If all else remains the same, which of these will make a confidence interval for a proportion wider? I. Increase the confidence level. II. Increase the sample size. III. Increase the margin of error. A. I only B. III only C. I and III D. II and III E. I, II, and III 2. The power of a test is A. the probability of rejecting the null hypothesis. B. the probability of rejecting the alternative hypothesis. C. the probability of failing to reject the null hypothesis. D. the probability of failing to reject the alternative hypothesis. E. the probability that you will make the correct decision.