Ch 15 - Inference in Practice

Question 1

The margin of error does not cover all errors:

Answer 1

The margin of error in a confidence interval covers only random sampling error.

Question 2

____ are often more serious than random sampling error (e.g., our elections polls). and the margin of error ___

Answer 2

Undercoverage, nonresponse or other forms of bias

does not take these into account at all.

For instance, most opinion polls have > 50% nonresponse. This is not taken into account in the margin of error.

Question 3

you may need a certain margin of error (e.g., drug trial, manufacturing specs). In many cases,

Answer 3

the population variability (s) is fixed, but we can choose the number of measurements (n).

using simple algebra, you can find what sample size is needed to obtain a desired margin of error.

Question 4

Answer 4

Question 5

Statistical significance only says whether the effect observed is

Answer 5

likely to be due to chance alone because of random sampling

Question 6

population effects in large and small samples

Answer 6

Because large random samples have small chance variation, very small population effects can be highly significant if the sample is large.

Because small random samples have a lot of chance variation, even large population effects can fail to be significant if the sample is small.

Question 7

Type I vs Type II error

Answer 7

A Type I error occurs when we reject the null hypothesis but the null hypothesis is actually true (incorrectly reject a true H0) .

Type II error occurs when we fail to reject the null hypothesis but the null hypothesis is actually false (incorrectly keep a false H0)

Question 8

The probability of making a Type I error (incorrectly rejecting a true H0) is the

Answer 8

significance level a

Question 9

The probability of making a Type II error (incorrectly keeping a false H0) is labeled ___

Answer 9

b, a computed value that depends on a number of factors.

Question 10

The power of a test is defined as ____

Answer 10

the value 1 − b.

Question 11

A Type II error is not definitive because

Answer 11

“failing to reject the null hypothesis” does not imply that the null hypothesis is true

Question 12

The power of a test of hypothesis is its

Answer 12

ability to detect a specified effect size (reject H0 when a given Ha is true) at significance level α.

Question 13

trade off of type 1 and type 2 errors

Answer 13

Question 14

What affects power?

Answer 14

Question 15

The probability of incorrectly rejecting H0 (Type I error) is the significance level a. If we set a = 5% and make multiple analyses, we can expect to make a Type I error about 5% of the time.

If you run only 1 analysis, this is not a problem.

If you try the same analysis with 100 random samples, you can expect

Answer 15

about 5 of them to be significant even if H0 is true.

(multiple - wrongly reject 5)

Question 16

The national average birth weight is 120 oz: N(unatl =120, sigma = 24 oz).
We want to be able to detect an average birth weight of 114 oz (5% lower than the national average).

What power would we get from an SRS of 100 babies born of poor mothers if we chose a significance level of 0.05?

Answer 16

80%

Question 17

You run a test of hypotheses for extra sensory perception on an individual chosen at random. You then run the same test on 19 other individuals also chosen at random. What’s wrong with that?

Answer 17

For a significance level a = 5%, you can expect that one individual will have a significant result just by chance even if extrasensory perception doesn’t exist.

Question 18

Answer 18

Using a significance level of 0.05, we can expect to get a Type I error 5% of the time we get a P-value.

Here the same analysis is done 20 times, one for each type of glioma. It is not surprising that one analysis turned up significant, because even if the null hypothesis of no association was true we would expect about 1 of the 20 analyses to yield a P-value less than 0.05.

Question 19

To use z procedures for a mean

Answer 19

Question 20

Angina is the severe pain caused by inadequate blood supply to the heart. Perhaps we can relieve angina by tying off (“ligation”) the mammary arteries to force the body to develop other routes to supply blood to the heart. Patients reported a statistically significant reduction in angina pain.

Problem?

Answer 20

This experiment was uncontrolled, so that the reduction in pain might be nothing more than the placebo effect. - No control

Statistical significance says that something other thanchance is at work, but it doesn’t say what that something is. b/c no control group

A significant P-value only says that the results cannot be explained by chance alone due to the random sampling process. It does not say what caused the results or that the results are important. Here the first study was so poorly designed that we could not tell what caused the significant reduction in angina pain (no control group).

Question 21

Power vs Alpha vs Betta

Answer 21

Betta - Type 2 error
Power - 1 - Betta
Alpha - Type 1 error