
Significance Tests and Decision Making
Authored by Anthony Clark
Mathematics
12th Grade

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11 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
A test of H0: µ=60 versus Ha: µ≠60 produces a sample mean of x-bar = 58 and a P-value of 0.04. At an α = 0.05 level, which of the following is an appropriate conclusion?
There is sufficient evidence to conclude that µ < 60.
There is sufficient evidence to conclude that µ = 60.
There is insufficient evidence to conclude that µ = 60.
There is insufficient evidence to conclude that µ ≠ 60
There is sufficient evidence to conclude that µ ≠ 60.
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
We want to test H0: µ = 1.5 vs. Ha : µ ≠ 1.5 at α = 0.05 . A 95% confidence interval for µ calculated from a given random sample is (1.4, 3.6). Based on this finding we
fail to reject H0
reject H0
cannot make any decision at all because the value of the test statistic is not available
cannot make any decision at all because the distribution of the population is unknown
cannot make any decision at all because (1.4, 3.6) is only a 95% confidence interval for µ
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The water diet requires you to drink two cups of water every half hour from the time you get up until you go to bed, but otherwise allows you to eat whatever you like. Four adult volunteers agree to test the diet. They are weighed prior to beginning the diet and after six weeks on the diet. The weights (in pounds) are (see photo). What would a Type II error be for this test of the water diet?
Concluding that the diet leads to weight loss when it doesn’t.
Concluding that the diet leads to weight loss when it really does.
Not concluding that the diet leads to weight loss when it does.
Not concluding that the diet leads to weight loss when it really doesn’t.
Drawing a conclusion from this test when the Normality condition has not been satisfied.
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
A researcher wishes to determine if people are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose previous research has established that the mean time needed for people to complete a certain maze (without music) is 40 seconds. The researcher, therefore, decides to test the hypotheses H0: µ = 40 versus Ha: µ < 40 , where µ is the time in seconds needed to complete the maze while listening to classical music. To do so, the researcher has 10,000 people complete the maze with classical music playing. The mean time for these people is x-bar = 39.92 seconds, and the P-value of his significance test is 0.0002. Which statement below best describes the appropriate conclusion to draw from this study?
The researcher has proved that listening to classical music substantially improves the time it takes to complete the maze.
The researcher has strong evidence that listening to classical music substantially improves the time it takes to complete the maze.
The researcher has moderate evidence that listening to classical music substantially improves the time it takes to complete the maze.
Although the researcher has obtained a statistically significant result, it appears to have little practical significance.
Since the P-value is greater than the reciprocal of the sample size, this is not a significant result.
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
The recommended daily Calcium intake for women over 21 (and under 50) is 1000 mg per day. The health services at a college are concerned that women at the college get less Calcium than that, so they take a random sample of female students in order to test the hypotheses H0: μ =1000 versus Ha: μ<1000. Prior to the study they estimate that the power of their test against the alternative Ha:μ=900 is 0.85. Which of the following is the best interpretation of this value?
The probability of making a Type II error.
The probability of rejecting the null hypothesis when the parameter value is 1000.
The probability of rejecting the null hypothesis when the parameter value is 900.
The probability of failing to reject the null hypothesis when the parameter value is 1000.
The probability of failing to reject the null hypothesis when the parameter value is 900.
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Which of the following describes a Type II error in this setting?
Concluding that the students are less fit (on average) than the general population when in fact they have equal fitness on average.
Not concluding that the students are less fit (on average) as the general population when in fact they are less fit (on average).
Not concluding that the students are less fit (on average) as the general population when in fact they have the same fitness (on average).
Concluding that the students are less fit (on average) than the general population, when, in fact, they are less fit (on average).
Concluding that the students have the same fitness (on average) when in fact they are more fit (on average).
7.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
A significance test was performed to test the null hypothesis H0: µ = 2 versus the alternative Ha: µ ≠ 2. A sample of size 28 produced a test statistic is t = 2.051. Assuming all conditions for inference were met, which of the following intervals contains the P-value for this test?
P < 0.01
0.01≤ P < 0.02
0.02 ≤ P < 0.025
0.025 ≤ P < 0.05
0.05 ≤ P < 0.10
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