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WorksheetsType I and II Errors/Tests
Total questions: 14
Worksheet time: 12mins
Which of the following best describes a Type II error?
The null is true but we mistakenly reject it.
The null is false but we mistakenly reject it.
The null is false but we fail to reject it.
The null is true but we fail to reject it.
A tire manufacturer claims that one particular type of tire will last at least 50,000 miles. A group of angry customers do not believe this is so. They take a sample of 14 tires to test if the mean mileage of the tires is really less than 50,000. What set of hypotheses are they interested in testing?
a) H0: m = 50,000 vs. Ha: m < 50,000
b)H0: x̅ = 50,000 vs. Ha: x̅ < 50,000
c)H0: m = 50,000 vs. Ha: m ≠ 50,000
d)H0: m = 50,000 vs. Ha: m > 50,000
An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7 years with a standard deviation of 2 years. Do the data provide convincing evidence that the mean time of employment for the population of postal workers has changed from the value of 7.5 that was true 20 years ago? What conclusion should you draw at the 5% significance level?
There is convincing evidence that the mean time working with the postal service has changed
There is not convincing evidence that the mean time working with the postal service has changed
There is convincing evidence that the mean time working with the postal service is still 7.5 years
There is convincing evidence that the mean time working with the postal service is now 7 years
We cannot draw a conclusion at the 5% significance level. The sample size is too small
The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that
z requires that the sample size be large
z requires that you know the population standard deviation σ
z requires that the data come from a random sample or randomized experiment
z requires that the population distribution be perfectly Normal
z can only be used for proportion
In a study of heart surgery, one issue was the effect of drugs called beta-blockers on the pulse rate of patients during surgery. The available subjects were divided at random into two groups of 30 patients each. One group received a beta-blocker; the other group received a placebo. The pulse rate of each patient at a critical point during the operation was recorded. The treatment group had mean 65.2 and standard deviation 7.8. For the control group, the mean was 70.3 and the standard deviation was 8.3.
Perform an appropriate significance test to see if beta-blockers reduce the pulse rate.
1-sample t-test
paired t-test (mean difference)
Neither
A listening test was administered to Spanish teachers before and after an institute designed to improve Spanish listening skills. The maximum possible score on the test was 36. The Pre- and Post-test results for each subject are listed below:
Sub 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Pre 30 28 31 26 20 30 34 15 28 20 30 29 31 29 34 20 26 25 31
Pos 29 30 32 30 16 25 31 18 33 25 32 28 34 32 32 27 28 29 32
What test would you conduct to determine if the institute improved listening skills at the 5% significance level.
1-sample t-test
paired t-test (mean difference)
Neither
In an experiment to compare anxiety levels induced between looking at real spiders and pictures of spiders, data was collected from 12 people with a fear of spiders (arachnophobia). Each participant was shown a real spider and a picture of a spider in a randomly assigned order. An anxiety score was recorded for each real spider and each picture. What test would you conduct to determine if there is evidence to conclude that real spiders induce more anxiety than pictures of spiders?
1-sample t-test
paired t-test (mean difference)
Neither
