Researchers are interested in evaluating the effect of a natural product on reducing blood pressure. This will be done by comparing the mean reduction in blood pressure of a treatment (natural product) group and a placebo group using a two-sample t-test. The researchers would like to be able to detect whether the natural product reduces blood pressure by at least points more, on average than the placebo. If groups of size are used in the experiment, a two-sample t-test using role="math" localid="1650436089340" will have a power of to detect a -point difference in mean blood pressure reduction. If the researchers want to be able to detect a -point difference instead, then the power of test
(a) would be less than .
(b) would be greater than .
(c) would still be .
(d) could be either less than or greater than , depending on whether the natural product is effective.
(e) would vary depending on the standard deviation of the data.
If the researchers want to be able to detect a -point difference instead, then the power of test is option (a) would be less than .
The size of group is
The larger difference is easier to detect and thus has a higher power.
We'd like to see how effective a natural product is at lowering blood pressure. As a result, the smaller the difference between
Hence if the test's power is for alternative hypothesis.
Then, For alternate hypothesis, the test's power will be greater than
Since the difference is decreased from to , the power will also decrease and thus the correct answer is (a).
Since the difference is decrease from 7 to 5, power would not be greater than 80%. It cannot depending on the standard deviation of the data. Therefore option b, c, d and e are incorrect answers.
Coaching and SAT scores What we really want to know is whether coached students improve more than uncoached students and whether any advantage is large enough to be worth paying for. Use the information above to answer these questions:
(a) Is there good evidence that coached students gained more on average than uncoached students? Carry out a significance test to answer this question.
(b) How much more do coach students gain on the average? Construct and interpret a confidence interval.
(c) Based on your work, what is your opinion: do you think coaching courses are worth paying for?
Your teacher brings two bags of colored goldfish crackers to class. She tells you that Bag has red crackers and Bag has red crackers. Each bag contains more than crackers. Using a paper cup, your teacher takes an SRS of crackers from Bag 1 and a separate SRS of crackers from Bag . Let be the difference in the sample proportions of red crackers.
What is the shape of the sampling distribution of ? Why?
As part of the Pew Internet and American Life Project, researchers surveyed a random sample of teens and a separate random sample of young adults. The teens, said that they own an iPod or MP3 player. For the young adults, this figure was . Is there a significant difference between the population proportions? State appropriate hypotheses for a significance test to answer this question. Define any parameters you use
A large clinical trial of the effect of diet on breast cancer assigned women at random to either a normal diet or a low-fat diet. To check that the random assignment did produce comparable groups, we can compare the two groups at the start of the study. Ask if there is a family history of breast cancer: of the women in the low-fat group and of the women in the control group said “Yes.” If the random assignment worked well, there should not be a significant difference in the proportions with a family history of breast cancer.
(a) How significant is the observed difference? Carry out an appropriate test to help answer this question.
(b) Describe a Type I and a Type II error in this setting. Which is more serious? Explain.
A random sample of 200 New York State voters included 88 Republicans, while a random sample of 300 California voters produced 141 Republicans. Which of the following represents the confidence interval that should be used to estimate the true difference in the proportions of Republicans in New York State and California?
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