Significance Tests and Confidence Intervals Answers

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Based upon the confidence interval, can the sleep scientist reject the null hypothesis?

A
She can reject the null hypothesis at = 0.05 because 7.5 is not contained in the 95% confidence interval.
Option A
B
She cannot reject the null hypothesis at = 0.05 because 7.5 is not contained in the 95% confidence interval.
Option B
C
She can reject the null hypothesis at = 0.01 because 7.5 is not contained in the 95% confidence interval.
Option C
D
She cannot reject the null hypothesis at = 0.01 because 7.5 is not contained in the 95% confidence interval.
Option D
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one-sided✔ two-sided

Answers:
When a test is ::two-sided
If the value of interest falls outside a 95% confidence interval, we will reject the null hypothesis at the = significance level.:0.05
If the value of interest falls outside a 99% confidence interval, we will reject the null hypothesis at the = significance level.:0.01
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0.01✔ 0.050.10

A
0.01
B
✔ 0.05
C
0.10
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✔ 0.010.050.10

A
✔ 0.01
B
0.05
C
0.10
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Based on the confidence interval, what conclusion would you make for a test of these hypotheses?

Answers:
The 99% confidence interval include as a plausible value, so we would H0. We convincing evidence that the true mean hours of NREM sleep per night for adults who use a weighted blanket 5 hours.:does not
The 99% confidence interval include as a plausible value, so we would H0. We convincing evidence that the true mean hours of NREM sleep per night for adults who use a weighted blanket 5 hours.:5
The 99% confidence interval include as a plausible value, so we would H0. We convincing evidence that the true mean hours of NREM sleep per night for adults who use a weighted blanket 5 hours.:reject
The 99% confidence interval include as a plausible value, so we would H0. We convincing evidence that the true mean hours of NREM sleep per night for adults who use a weighted blanket 5 hours.:have
The 99% confidence interval include as a plausible value, so we would H0. We convincing evidence that the true mean hours of NREM sleep per night for adults who use a weighted blanket 5 hours.:is different from
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✔ 55.15.87.5

A
✔ 5
B
5.1
C
5.8
D
7.5
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✔ rejectfail to reject

A
✔ reject
B
fail to reject
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✔ havedo not have

A
✔ have
B
do not have
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equals✔ is different fromis greater thanis less than

A
equals
B
✔ is different from
C
is greater than
D
is less than
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Based on the confidence interval, what conclusion would you make for a test of these hypotheses?

Answers:
The 95% confidence interval include as a plausible value, so we H0. We convincing evidence that the true mean amount of REM sleep per night for babies 6 hours.:does
The 95% confidence interval include as a plausible value, so we H0. We convincing evidence that the true mean amount of REM sleep per night for babies 6 hours.:6
The 95% confidence interval include as a plausible value, so we H0. We convincing evidence that the true mean amount of REM sleep per night for babies 6 hours.:fail to reject
The 95% confidence interval include as a plausible value, so we H0. We convincing evidence that the true mean amount of REM sleep per night for babies 6 hours.:do not have
The 95% confidence interval include as a plausible value, so we H0. We convincing evidence that the true mean amount of REM sleep per night for babies 6 hours.:is different from
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5.45✔ 66.258

A
5.45
B
✔ 6
C
6.25
D
8
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reject✔ fail to reject

A
reject
B
✔ fail to reject
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have✔ do not have

A
have
B
✔ do not have
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equals✔ is different fromis greater thanis less than

A
equals
B
✔ is different from
C
is greater than
D
is less than
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The power of this test to reject 7.5 hours, if the true mean is , is 0.57.

Answers:
If the true amount of sleep per day for highly productive individuals is = , there is a 0.57 probability that the scientist will find convincing evidence for .:mean
If the true amount of sleep per day for highly productive individuals is = , there is a 0.57 probability that the scientist will find convincing evidence for .:7
If the true amount of sleep per day for highly productive individuals is = , there is a 0.57 probability that the scientist will find convincing evidence for .:the alternative hypothesis
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✔ 77.5

A
✔ 7
B
7.5
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✔ the alternative hypothesisthe null hypothesis

A
✔ the alternative hypothesis
B
the null hypothesis
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The power of a test is the probability that the test will find convincing evidence for Ha when a specific alternative value of the parameter is true.Stated another way, power is equivalent to

A
rejecting H0 when you should reject H0.
B
failing to reject H0 when you should reject H0.
C
rejecting H0 when you should not reject H0.
D
failing to reject H0 when you should not reject H0.
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A test of the hypotheses H0: = 7.5 versus Ha: < 7.5 has low power. What can the researcher do to increase the power of the test to reject the null hypothesis if = 7? Check all that apply.The researcher can increase the sample size.The researcher can cut the sample size in half.The researcher can decrease the significance level of the test.The researcher can increase the significance level of the test.The researcher can try to decrease the probability of making a Type II error.The researcher can try to increase the probability of making a Type II error.

Question illustration
A
The researcher can increase the sample size.
B
The researcher can cut the sample size in half.
C
The researcher can decrease the significance level of the test.
D
The researcher can increase the significance level of the test.
E
The researcher can try to decrease the probability of making a Type II error.
F
The researcher can try to increase the probability of making a Type II error.

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