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Chapter 9: Q. 62. (page 584)
Which of the following confidence intervals would lead us to reject in favor of at the significance level?
a.
b.
c.
d.
e. None of these
The required correct option is
The confidence interval to reject the null hypothesis at the significance level is
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Fast connection? How long does it take for a chunk of information to travel
from one server to another and back on the Internet? According to the site
internettrafficreport.com, the average response time is 200 milliseconds (about one-fifth of a second). Researchers wonder if this claim is true, so they collect data on response times (in milliseconds) for a random sample of 14 servers in Europe. A graph of the data reveals no strong skewness or outliers.
a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.
b. Check conditions for performing the test in part (a).
c. The 95% confidence interval for the mean response time is 158.22 to 189.64
milliseconds. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 5% significance level?
d. Do we have convincing evidence that the mean response time of servers in the United States is different from 200 milliseconds? Justify your answer.
A company that manufactures classroom chairs for high school students
claims that the mean breaking strength of the chairs is 300 pounds. One of the chairs collapsed beneath a 220-pound student last week. You suspect that the manufacturer is exaggerating the breaking strength of the chairs, so you would like to perform a test of where μ is the true mean breaking strength of this company’s classroom chairs.
a. The power of the test to detect that μ=294 based on a random sample of 30
chairs and a significance level of α=0.05 is 0.71. Interpret this value.
b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).
c. Describe two ways to increase the power of the test in part (a).
Jump around Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was inches. They wondered if the average vertical jump of students at their school differed from inches, so they obtained a list of student names and selected a random sample of students. After contacting these students several times, they finally convinced them to allow their vertical jumps to be measured. Here are the data (in inches):
Do these data provide convincing evidence at the level that the average vertical jump of students at this school differs from 15 inches?
Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.
For a poll of adults, the variation due to sampling error is no more than
percentage points either way. The error margin is said to be valid at the
confidence level. This means that, if the same questions were repeated in polls, the results of at least surveys would be within percentage points of the results of this survey.
Making conclusions A student performs a test of versus at significance level and gets a -value of
The student writes: “Because the P-value is large, we accept . The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.
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