Statistics Help Please!?
Question by Katherine: Statistics Help Please!?
There is an old saying “Statistics means never having to say you’re certain.” In the context of hypothesis tests, why might this be true?
A. It’s just a joke on statisticians, and literally means nothing.
B. It isn’t — if I get a P-value of 0.0000001 (or less) I’m sure the null hypothesis is wrong.
C. To be totally confident, I would need a P-value of exactly 0.000000000, which is impossible.
2. Physical fitness and health tests include various biological measures such as heart rate during exercise, blood pressure, blood tests and more. Suppose that the population of the physical fitness and health scores of all high school seniors who took a standard physical fitness and health test this year follows a normal distribution with mean ? = 480 and standard deviation ? = 90. You read a report that claims that 10,000 students who took part in a national program for improving one’s physical fitness and health score had significantly better scores (at the 0.05 level of significance) than the population as a whole. In order to determine if the improvement is of practical significance (beyond simple statistical significance), one should
A. find out the P-value and the actual mean score of the 10,000 students.
B. use a two-sided test rather than the one-sided test implied by the report.
C. find out the actual P-value.
3. A biologist wants to know if a new method for implanting organs will help the implanted organ to be accepted. He tries the method on a sample of 35 mice and finds a P-value of 0.078 when comparing the success of the implantation to that of another random identical group of mice treated with the standard method. Another experiment showed a P-value of 0.006 with a sample of 150 mice (different from the last group), indicating the implantations were better, with the new method. What’s the difference?
A.There were probably some outliers that affected the analysis.
B. The second group had more mice — a larger sample size.
C. The second group of mice was in a better physical condition
4. A biologist wants to know if a novel drug treatment can have a positive affect on Alzheimer’s disease. He tested the new drug on a sample of rats, previously exposed to different experimental treatments and drugs. Eight hundred rats were tested, with each rat given a score for the effect of the drug. The mean score for this sample was 0.805. The biologist further calculated the standard deviation of the sample scores, calculated a 95% confidence interval and declared “The mean population score for the new drug is between ?0.78 and 0.83.”
A. this is a valid interval, so the biologist could be right.
B. Because of the way the experiment was conducted, the results are invalid.
C. We can’t say for certain that the mean score is between 0.78 and 0.83 because it is a 95% confidence interval
Best answer:
Answer by Guy
The answer to question 1 is C because a p-value is the probability of making a type I error, which means it would have to be 0 in order for there to be no chance of making that error.
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