9.4 Rare Events, the Sample, and the Decision and Conclusion
Rare-event reasoning behind a p-value, comparing it against a preset significance level, and wording the decision without overclaiming proof.
Statistics, 9.4 Rare Events, the Sample, and the Decision and Conclusion
9 exercises
9.4 Exercise 2
This memory aid relates a p-value less than the established alpha (the p is low) as rejecting the null hypothesis and, likewise, relates a p-value higher than the established alpha (the p is high) as not rejecting the null hypothesis.
Fill in the blanks.
Reject the null hypothesis when ______________________________________.
The results of the sample data _____________________________________.
Do…
9.4 Exercise 3
It’s a Boy Genetics Labs, a genetics company, claims their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows:
H0: p = 0.50, Ha: p > 0.50
α = 0.01
p-value = 0.025
Interpret the results and state a conclusion in simple, nontechnical terms.
9.4 Exercise 5
The probability of winning the grand prize at a particular carnival game is 0.005. Is the outcome of winning very likely or very unlikely?
9.4 Exercise 7
It is believed that the mean height of high school students who play basketball on the school team is 73 inches 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 alt…
9.4 Exercise 11
What should you do if α = p-value?
9.4 Exercise 13
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…
9.4 Exercise 15
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…
9.4 Exercise 17
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…
9.4 Exercise 19
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…
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