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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
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?
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
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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