# Hypothesis Statistics Question

3. Why do experimenters test hypotheses they think are false?(relevant section)

4. State the null hypothesis for:

a. An experiment testing whether echinacea decreases the

length of colds.

b. A correlational study on the relationship between brain size

and intelligence.

c. An investigation of whether a self-proclaimed psychic can

predict the outcome of a coin flip.

d. A study comparing a drug with a placebo on the amount of

pain relief. (A one-tailed test was used.)

5. Assume the null hypothesis is that µ = 50 and that the

graph shown below is the sampling distribution of the mean (M).

Would a sample value of M= 60 be significant in a two-tailed test

at the .05 level? Roughly what value of M would be needed to be

significant? (relevant section & relevant section)

6. A researcher develops a new theory that predicts that

vegetarians will have more of a particular vitamin in their

blood than non-vegetarians. An experiment is conducted and

vegetarians do have more of the vitamin, but the difference is

not significant. The probability value is 0.13. Should the

experimenter’s confidence in the theory increase, decrease, or

stay the same? (relevant section)

7. A researcher hypothesizes that the lowering in cholesterol

associated with weight loss is really due to exercise. To test

this, the researcher carefully controls for exercise while

comparing the cholesterol levels of a group of subjects who

lose weight by dieting with a control group that does not diet.

The difference between groups in cholesterol is not significant.

Can the researcher claim that weight loss has no effect?

(relevant section)

8. A significance test is performed and p = .20. Why can’t

the experimenter claim that the probability that the null

hypothesis is true is .20?

9. You choose an alpha level of .01 and then analyze your

data. (a) What is the probability that you will make a Type I error

given that the null hypothesis is true? (b) What is the probability that

you will make a Type I error given that the null hypothesis is false?

1. When would the mean grade in a class on a final exam be

considered a statistic? When would it be considered a

parameter? (relevant section)

2. Define bias in terms of expected value. (relevant section)

3. Is it possible for a statistic to be unbiased yet very imprecise?

How about being very accurate but biased? (relevant section)

4. Why is a 99% confidence interval wider than a 95%

confidence interval? (relevant section & relevant section)

5. When you construct a 95% confidence interval, what are you

95% confident about? (relevant section)

6. How does the t distribution compare with the normal

distribution? How does this difference affect the size of

confidence intervals constructed using z relative to those

constructed using t? Does sample size make a difference?

(relevant section)

7. A population is known to be normally distributed with a

standard deviation of 2.8. (a) Compute the 95% confidence

interval on the mean based on the following sample of nine:

8, 9, 10, 13, 14, 16, 17, 20, 21. (b) Now compute the 99%

confidence interval using the same data. (relevant section)

8. A person claims to be able to predict the outcome of flipping a

coin. This person is correct 16/25 times. Compute the 95%

confidence interval on the proportion of times this person can

predict coin flips correctly. What conclusion can you draw

about this test of his ability to predict the future? (relevant

section)

9. The scores of a random sample of 8 students on a physics test

are as follows: 60, 62, 67, 69, 70, 72, 75, and 78.

1. Test to see if the sample mean is significantly different

from 65 at the .05 level. Report the t and p values.

2. The researcher realizes that she accidentally recorded

the score that should have been 76 as 67. Are these

corrected scores significantly different from 65 at

the .05 level? (relevant section)

10. A new test was designed to have a mean of 80 and a standard

deviation of 10. A random sample of 20 students at your school

take the test, and the mean score turns out to be 85. Does this

score differ significantly from 80? To answer this problem, you

may want to use the Normal Distribution Calculator.(relevant

section)

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