Rare Events, the Sample, and the Decision and Conclusion Quiz
The question sheet
Reveal any answer as you study-
When a p-value is almost zero, as in the basketball player height test, this outcome is considered a:
- Common event
- Impossible event
- Guaranteed event
- Rare event
Reveal answer
Answer: Rare event
Source evidence
PDF page 523: with a standard deviation of 1.8 inches. A random sample of 40 players is chosen. The sample mean was 71 inches, and the sample standard deviation was 1.5 inches. Do the data support the claim that the mean height is less than 73 inches? The p-value is almost zero. State the null and alternative hypotheses and interpret the p-value.
PDF page 523: this considered a rare or common event? Why?
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In the marathon runner survey, the sample mean length of time they had been running was:
- 75 years
- 6.3 years
- 17.4 years
- 15 years
Reveal answer
Answer: 17.4 years
Source evidence
PDF page 523: 48. A random survey of 75 long-term marathon runners revealed that the mean length of time they have been
PDF page 524: running is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time is likely to be 15 years.
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In the marathon runner example, the standard deviation reported was:
- 6.3 years
- 17.4 years
- 2.4 years
- 15 years
Reveal answer
Answer: 6.3 years
Source evidence
PDF page 524: running is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time is likely to be 15 years.
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The marathon runner test seeks to determine if the population mean time is likely to be:
- 75 years
- 6.3 years
- 17.4 years
- 15 years
Reveal answer
Answer: 15 years
Source evidence
PDF page 524: running is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time is likely to be 15 years.
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One question asked about the marathon test is whether it is a test of:
- One mean or proportion
- Correlation
- Two variances
- Independence
Reveal answer
Answer: One mean or proportion
Source evidence
PDF page 524: a. Is this a test of one mean or proportion?
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A hypothesis test can be classified according to its tails as:
- Rare or common
- Nominal or ordinal
- Right, left, or two-tailed
- Discrete or continuous
Reveal answer
Answer: Right, left, or two-tailed
Source evidence
PDF page 524: c. Is this a right-tailed, left-tailed, or two-tailed test?
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In the homework study, the stated mean time students spend doing homework each week was:
- 1.5 hours
- 3 hours
- 1.8 hours
- 2.5 hours
Reveal answer
Answer: 2.5 hours
Source evidence
PDF page 523: Use the following information to answer the next seven exercises: Suppose that a recent article stated that the mean time students spend doing homework each week is 2.5 hours. A study was then done to see if the mean time has increased in the new century. A random sample of 26 students was taken. The mean length of time they did homework each week was three hours with a standard deviation of 1.8 hours. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of time doing homework each week has increased. Assume the distribution of homework times is approximately normal.
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In the homework study, the sample mean length of time doing homework was:
- 26 hours
- 2.5 hours
- 1.5 hours
- 3 hours
Reveal answer
Answer: 3 hours
Source evidence
PDF page 523: Use the following information to answer the next seven exercises: Suppose that a recent article stated that the mean time students spend doing homework each week is 2.5 hours. A study was then done to see if the mean time has increased in the new century. A random sample of 26 students was taken. The mean length of time they did homework each week was three hours with a standard deviation of 1.8 hours. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of time doing homework each week has increased. Assume the distribution of homework times is approximately normal.
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In the homework study, the known population standard deviation was:
- 1.5
- 2.5
- 3
- 1.8
Reveal answer
Answer: 1.5
Source evidence
PDF page 523: Use the following information to answer the next seven exercises: Suppose that a recent article stated that the mean time students spend doing homework each week is 2.5 hours. A study was then done to see if the mean time has increased in the new century. A random sample of 26 students was taken. The mean length of time they did homework each week was three hours with a standard deviation of 1.8 hours. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of time doing homework each week has increased. Assume the distribution of homework times is approximately normal.
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The homework study aimed to determine if the mean length of time doing homework had:
- Increased
- Stayed the same
- Become zero
- Decreased
Reveal answer
Answer: Increased
Source evidence
PDF page 523: Use the following information to answer the next seven exercises: Suppose that a recent article stated that the mean time students spend doing homework each week is 2.5 hours. A study was then done to see if the mean time has increased in the new century. A random sample of 26 students was taken. The mean length of time they did homework each week was three hours with a standard deviation of 1.8 hours. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of time doing homework each week has increased. Assume the distribution of homework times is approximately normal.
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The number of students sampled in the homework study was:
- 75
- 40
- 26
- 15
Reveal answer
Answer: 26
Source evidence
PDF page 523: Use the following information to answer the next seven exercises: Suppose that a recent article stated that the mean time students spend doing homework each week is 2.5 hours. A study was then done to see if the mean time has increased in the new century. A random sample of 26 students was taken. The mean length of time they did homework each week was three hours with a standard deviation of 1.8 hours. Suppose that it is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine if the mean length of time doing homework each week has increased. Assume the distribution of homework times is approximately normal.
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In the basketball height test, the sample mean height was:
- 1.5 inches
- 71 inches
- 73 inches
- 40 inches
Reveal answer
Answer: 71 inches
Source evidence
PDF page 523: with a standard deviation of 1.8 inches. A random sample of 40 players is chosen. The sample mean was 71 inches, and the sample standard deviation was 1.5 inches. Do the data support the claim that the mean height is less than 73 inches? The p-value is almost zero. State the null and alternative hypotheses and interpret the p-value.
Statistics
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