WorksheetsHypothesis testing and Errors
Total questions: 17
Worksheet time: 11mins
Reorder the following steps for Hypothesis testing.
State your research hypothesis as a null hypothesis (Ho) and alternate hypothesis (Ha).
Collect data in a way designed to test the hypothesis.
Perform an appropriate statistical test.
Decide whether to reject or fail to reject your null hypothesis.
Make a conclusion:
A Type I error occurs when
A test statistic is incorrect.
A null hypothesis is not rejected but should be rejected.
A null hypothesis is rejected but should not be rejected.
None of the options listed here.
A Type II error occurs when
A test statistic is incorrect.
A null hypothesis is not rejected but should be rejected.
A null hypothesis is rejected but should not be rejected.
None of the options listed here.
Selecting the significance level α will determine;
The probability of they type I error.
The probability of the type II error
The power of the test
None of the mentioned options.
Bottles of water have a label stating that the volume is 12 oz. A consumer group suspects the bottles are under‐filled and plans to conduct a test. A Type I error in this situation would mean
the consumer group concludes the bottles have less than 12 oz. when the mean actually is 12 oz.
the consumer group does not conclude the bottles have less than 12 oz. when the mean actually is less than 12 oz.
the consumer group has evidence that the label is incorrect.
None of the mentioned options
A Type I error can occur when the null hypothesis is
correct
incorrect
either correct or incorrect
neither correct or incorrect.
A Type II error can occur when the null hypothesis
correct
incorrect
either correct or incorrect
neither correct or incorrect.
If the significance level, α, is increased, then the chance of a Type I error will
remain the same.
decrease
increase
none of the above mentioned options.
If the significance level, α, is increased then the chance of a Type II error will
remain the same.
decrease
increase
none of the above mentioned options.
If the significance level, α, is increased then the power will
remain the same.
decrease
increase
none of the above mentioned options.
The power of a test can be increased by
choosing a smaller value of α
using a larger sample size
using a normal approximation
none of the mentioned options
Donated blood is tested for infectious diseases and other contaminants. Since most donated blood is safe, workers save time and money by testing batches of donated blood rather than testing individual samples. Workers perform a test to check if a certain toxin is present, and the entire batch is discarded if the toxin is detected. This is similar to using a null and an alternative hypothesis to determine whether to discard the batch. The hypotheses being tested could be stated as:
H0: The batch does not contain the toxin.
Ha: The batch contains the toxin.
Under which of the following conditions would the testers commit a Type II error?
The batch does not actually contain the toxin, and they conclude that it does not.
The batch does not actually contain the toxin, and they conclude that it it does.
The batch actually contains the toxin, and they conclude that it does.
The batch actually contains the toxin, and they conclude that it does not.
Donated blood is tested for infectious diseases and other contaminants. Since most donated blood is safe, workers save time and money by testing batches of donated blood rather than testing individual samples. Workers perform a test to check if a certain toxin is present, and the entire batch is discarded if the toxin is detected. This is similar to using a null and an alternative hypothesis to determine whether to discard the batch. The hypotheses being tested could be stated as:
H0: The batch does not contain the toxin.
Ha: The batch contains the toxin.
What would be the consequence of a Type I error in this context?
The batch is discarded when it actually contains the toxin.
The batch is discarded when it actually doesn't contain the toxin.
The batch is kept when it actually contains the toxin.
The batch is kept when it actually doesn't contain the toxin.
Regulations from the Environmental Protection Agency say that soil used in play areas should not have lead levels that exceed 400 parts per million (ppm). Before beginning construction at a new site, an agent will take a sample of soil and run a significance test on the mean lead level in the soil. If the mean lead level in the sample is significantly higher than 400 ppm then the soil is deemed unsafe and construction cannot continue. Here are the hypotheses for this test:
H0: μ≤400 ppm (soil is safe)
Ha: μ>400 ppm (soil is unsafe)
(where μ is the mean lead level in the soil at the new site).
Which of the following would be a Type I error in this setting?
The soil is actually safe, and the sample result is below 400 ppm so construction continues.
The soil is actually safe, and the sample result is significantly higher than 400 ppm so construction stops.
The soil is actually unsafe, and the sample result is below 400 ppm so construction continues.
The soil is actually unsafe, and the sample result is significantly higher than 400 ppm so construction stops.
A quality control expert wants to test the null hypothesis that a new solar panel is no more effective than the older model.
Under which of the following conditions would the expert commit a Type II error?
The new panel is actually more effective, and they don't conclude that it is more effective.
The new panel is actually no more effective, and they conclude that it is more effective.
The new panel is actually more effective, and they conclude that it is more effective.
The new panel is actually no more effective, and they don't conclude that it is more effective.
A significance test is going to be performed using a significance level of α = 0.05 Suppose that the null hypothesis is actually true.
If the significance level was lowered to α = 0.01, which of the following would be true?
The probability of a Type I error would increase.
The probability of a Type I error would decrease.
The probability of a Type I error would stay the same.
We don't have enough information to reason about Type I error probabilities.
Employees at a health club do a daily water quality test in the club's swimming pool. If the level of contaminants is too high, then they temporarily close the pool to perform a water treatment.
We can state the hypotheses for their test as
H0: The water quality is acceptable vs. Ha: The water quality is not acceptable.
What would be the consequence of a Type I error in this setting? (a)
What would be the consequence of a Type II error in this setting? (b)
In terms of safety, which error has the more dangerous consequences in this setting? (c)
Since one error involves greater safety concerns, the club is considering using a value for α other than 0.05 for the water quality significance test. What significance level should they use to reduce the probability of the more dangerous error? (d)
