# 0.2 Practice tests (1-4) and final exams  (Page 17/36)

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11 . What is the degrees of freedom ( df ) for this study?

12 . For a two-tailed 95% confidence interval, what is the appropriate t -value to use in the formula?

13 . What is the 95% confidence interval?

14 . What is the 99% confidence interval? Round to two decimal places.

15 . Suppose your sample size had been 30 rather than 20. What would the 95% confidence interval be then? Round to two decimal places

## 8.3: confidence interval for a population proportion

Use this information to answer the next four exercises. You conduct a poll of 500 randomly selected city residents, asking them if they own an automobile. 280 say they do own an automobile, and 220 say they do not.

16 . Find the sample proportion and sample standard deviation for this data.

17 . What is the 95% two-sided confidence interval? Round to four decimal places.

18 . Calculate the 90% confidence interval. Round to four decimal places.

19 . Calculate the 99% confidence interval. Round to four decimal places.

Use the following information to answer the next three exercises. You are planning to conduct a poll of community members age 65 and older, to determine how many own mobile phones. You want to produce an estimate whose 95% confidence interval will be within four percentage points (plus or minus) the true population proportion. Use an estimated population proportion of 0.5.

20 . What sample size do you need?

21 . Suppose you knew from prior research that the population proportion was 0.6. What sample size would you need?

22 . Suppose you wanted a 95% confidence interval within three percentage points of the population. Assume the population proportion is 0.5. What sample size do you need?

## 9.1: null and alternate hypotheses

23 . In your state, 58 percent of registered voters in a community are registered as Republicans. You want to conduct a study to see if this also holds up in your community. State the null and alternative hypotheses to test this.

24 . You believe that at least 58 percent of registered voters in a community are registered as Republicans. State the null and alternative hypotheses to test this.

25 . The mean household value in a city is \$268,000. You believe that the mean household value in a particular neighborhood is lower than the city average. Write the null and alternative hypotheses to test this.

26 . State the appropriate alternative hypothesis to this null hypothesis: H 0 : μ = 107

27 . State the appropriate alternative hypothesis to this null hypothesis: H 0 : p <0.25

## 9.2: outcomes and the type i and type ii errors

28 . If you reject H 0 when H 0 is correct, what type of error is this?

29 . If you fail to reject H 0 when H 0 is false, what type of error is this?

30 . What is the relationship between the Type II error and the power of a test?

31 . A new blood test is being developed to screen patients for cancer. Positive results are followed up by a more accurate (and expensive) test. It is assumed that the patient does not have cancer. Describe the null hypothesis, the Type I and Type II errors for this situation, and explain which type of error is more serious.

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