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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Members of the city council want to know if a majority of city residents supports a increase in the sales tax to fund road repairs. To investigate, they survey a random sample of city residents and use the results to test the following hypotheses:
where is the proportion of all city residents who support a increase in the sales tax to fund road repairs.
In the sample, , The resulting -value is . What is the correct interpretation of this -value?
a. Only of the city residents support the tax increase.
b. There is an chance that the majority of residents supports the tax increase.
c. Assuming that of residents support the tax increase, there is an probability that the sample proportion would be or greater by chance alone.
d. Assuming that more than of residents support the tax increase, there is an probability that the sample proportion would be or greater by chance alone.
e. Assuming that of residents support the tax increase, there is an chance that the null hypothesis is true by chance alone.
Don't argue! A Gallup poll report revealed that of teens said they seldom or never argue with their friends. Yvonne wonders whether this result holds true in her large high school, so she surveys a random sample of students at her school.
state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest
Fire the coach!A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on emails he has received from alumni in the past three months. The college’s athletic director wants to perform a test of versus , where = the true proportion of the college’s alumni who favor firing the coach. Check if the conditions for performing the significance test are met.
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).
Battery life A tablet computer manufacturer claims that its batteries last an average of 10.5 hours when playing videos. The quality-control department randomly selects 20 tablets from each day’s production and tests the fully charged batteries by playing a video repeatedly until the battery dies. The quality control department will discard the batteries from that day’s production run if they find convincing evidence that the mean battery life is less than 10.5 hours. Here are a dot plot and summary statistics of the data from one day:
a. State appropriate hypotheses for the quality-control department to test. Be sure to define your parameter.
b. Check if the conditions for performing the test in part (a) are met.
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