STATS ch10

this is more precise but gives less confidence

A point estimate

this is the probability of a Type I error.

The alpha level

What is the decision to use the unit normal (i.e., z) distribution versus the student's t distributions as the frequency distribution for hypothesis testing based upon?

The decision to use the unit normal (i.e., z) distribution versus the student's t distributions as the frequency distribution for hypothesis testing is based on the understanding that when the standard deviation of the population is unknown, the critical values cannot come from the unit normal z distributions (whose formula requires we know the value of σ) but instead the t distribution requires we use the sample estimate (s). Since "s" is not exactly equal to "σ", we replace the z-distribution with the t-distribution to make up for the imprecision in point-estimating "σ" from "s".

this consists of sample means with very low probability of occurring if the null hypothesis is true

The region of rejection

this is determined by alpha level, not sample size

The region of rejection

this is inversely related to sample size

The standard erro

Zobs = = + 1.50, zcv = ± 1.96 1.50 < 1.96 State your decision regarding the null hypothesis.

The z-score we obtained is in the region of retention; thus, we fail to reject the null hypothesis. Similarly, the observed sample mean of 84 also lies in the region of retention (it is in between both mean critical values of 77.08 and 84.92). We can conclude that the observed sample mean is not significantly different from the Null Hypothesized population mean.

12. Suppose that in a particular experiment there are two critical values = 155.2 and = 177.4. Furthermore, suppose that = 181.1. We should a. reject the null hypothesis b. reject the alternative hypothesis c. reject the rejection region d. reject the standard error

a

13. In general, the null hypothesis states that the treatment has no effect on the population mean. a. true b. false

a

13. Which is the smallest in absolute value? a. zcv in a directional test with α = .05 b. zcv in a directional test with α = .01 c. zcv in a nondirectional test with α = .05 d. zcv in a nondirectional test with α = .01

a

15. If the obtained data are in the region of rejection, the correct decision is to: a. reject the null hypothesis b. reject the alternative hypothesis c. accept the alternative hypothesis d. fail to accept the alternative hypothesis

a

16. A type I error occurs when a researcher concludes that a treatment has an effect, but, in fact, the treatment has no effect. a. true b. false c. This is a Type II error d. Not enough information given

a

17. The alpha level determines the risk of a Type I error a. true b. false

a

18. If a sample is located in the region of rejection with = .01, then the sample would definitely be in the region of rejection if the alpha is changed to = .05. a. true b. false c. unable to say

a

22. If the alpha is increased from = .01 to = .05, what happens to the size of the region of rejection? a. it increases b. it decreases c. the alpha level has no influence on the size of the region of rejection

a

22. If the mean as specified by the null hypothesis does not lie in the confidence interval, we would a. reject the null hypothesis b. fail to reject the null hypothesis c. reject the alternative hypothesis d. conclude that hypothesis testing has very little to do with the information provided by a confidence interval

a

26. A Type I error means that a researcher has ______. a. falsely concluded that a treatment has an effect b. correctly concluded that a treatment has no effect c. falsely concluded that a treatment has no effect d. correctly concluded that a treatment has an effect

a

27. A population is known to have a mean of = 45. If a researcher predicts that the experimental treatment will produce a decrease in the scores, then the null hypothesis for a onetailed test would state ______. a. μ ≥ 45 b. μ ≤ 45 c. ! ≤ 45 d. ! ≥ 45

a

29. The power (1 - ) of a hypothesis test is defined as: a. the probability that the test will reject H0 if there is a real treatment effect b. the probability that the test will fail to reject H0 if the treatment has no effect c. the probability that the test will reject H0 if the treatment has no effect d. the probability that the test will fail to reject H0 if there is a real treatment effect

a

3. (From ReviewMaster) If the raw effect size is 10, the standard deviation is 20, and the sample size is 25, the effect size index d is what? a. .5 b. 1.0 c. 2.0 d. 2.5

a

3. A population has a = 50 and a standard deviation of 10. What is the standard error of the sampling distribution of means if samples of size n = 25 are selected from this population? a. 2 b. 5 c. 2.5 d. 0.4

a

31. The larger the value for df, the more a t distribution resembles a normal distribution a. true b. false

a

32. In a t distribution, the size of the estimated standard error is partially determined by the size of sample variance a. true b. false

a

32. Which of the following is a measure of practical significance? a. the effect size index d b. level of significance α c. probability of making a Type II error β d. power = 1 - β

a

42. If the mean as specified by the null hypothesis does not lie in the confidence interval, we would: a. reject the null hypothesis b. fail to reject the null hypothesis c. reject the alternative hypothesis d. conclude that hypothesis testing has very little to do with the information provided by a confidence interval

a

5. The critical value of a statistic a. marks the beginning of the rejection region b. is what you see in the data prior to performing any computations c. is a computed statistic of a sample d. is a computed parameter

a

7. The standard error of the mean can never be greater than the standard deviation of the population. a. True b. false c. Not enough information given d. They are always equal

a

1. A population distribution has a μ= 80 and σ= 6. If a z-score of z= +2.00, this means that the value of the of score X is: a. 2 points below the mean b. 92 c. 2 points above the mean d. 82

b

11. Suppose that in a particular experiment there are two critical values = 155.2 and = 177.4. The hypothesis being tested is a. directional b. nondirectional c. either directional or nondirectional (impossible to tell) d. neither directional nor nondirectional

b

12. If other factors are held constant, the standard error of the mean will _____ as the sample size increases. a. increase b. decrease c. stay constant

b

14. In a hypothesis test, the region of rejection consists of sample outcomes that have a high probability of occurring if the null hypothesis is true. a. true b. false

b

14. Other things being equal, the critical value for a directional test is the critical value for a nondirectional test. a. larger than b. smaller than c. the same as

b

15. Other things being equal, the critical value for a test with α = .05 is the critical value for a test with α = .01. a. larger than b. smaller than c. the same as

b

16. Other things being equal, the critical value for a test when σ is known is the critical value for a test when σ is unknown. a. larger than b. smaller than c. the same as

b

19. If a hypothesis test results in rejecting the null hypothesis, then the researcher must conclude: a. the treatment does not have a significant effect b. the treatment does have a significant effect

b

2. You wrote two exams, one in statistics and the other in sociology. You scored 5 points below the mean in both exams. What can you say about your scores? a. Both of your z-scores are positive b. Both of your z-scores are negative c. 55% of the scores are above you d. There is not enough information to say.

b

20. In general, the larger the variance (or standard deviation), the more likely you are to reject the null hypothesis. a. true b. false

b

23. Assume that for a particular experiment, the null hypothesis is H0: μ = 50, σ is not known, and the test is nondirectional. We collect a sample of size n = 16, and compute the following statistics from the sample data: = 54; s = 8.0; s2 = 64.0 (you may not need to know all these statistics). Then the raw effect size is a. 54 b. 4 c. .5 d. 2.0

b

24. With sigma known, a hypothesis test is being used to evaluate a treatment effect with = .05. If the sample data produces a z-score of zobs = -2.24, then what is the correct decision? a. reject the null hypothesis and conclude the treatment has no effect b. reject the null hypothesis and conclude the treatment has an effect c. fail to reject the null and conclude the treatment has no effect d. fail to reject the null and conclude the treatment has an effect

b

25. If the critical values for a hypothesis test are z = ± 1.96, and if the obtained z-score for the sample data is zobs = -1.90, what is the correct statistical decision? a. fail to reject H1 b. fail to reject H0 c. Reject H1 d. reject H0

b

26. Assume that for a particular experiment, the null hypothesis is H0: μ = 50, σ is not known, and the test is nondirectional. We collect a sample of size n = 16, and compute the following statistics from the sample data: = 54; s = 8.0; s2 = 64.0 (you may not need to know all these statistics). The number of degrees of freedom are a. 8 b. 15 c. 16 d. unnecessary in this study

b

27. Assume that for a particular experiment, the null hypothesis is H0: μ = 10, σ is known to be 3, and the test is nondirectional. We collect a sample of size n = 9, and compute the following statistics from the sample data: = 12; s = 4.0; s2 = 16.0 (you may not need to know all these statistics). Then the raw effect size is a. 12 b. 2 c. .5 d. .667

b

28. A researcher administers a treatment to n=25 and uses a hypothesis test to evaluate the effect of a treatment. The hypothesis tests produces a z-score of zobs = +2.77. Assuming the researcher is using a two-tailed test: a. the researcher rejects the null with an = .05 but not with an = .01 b. the researcher should reject the null hypothesis with either a = .05 or a = .01 c. the researcher should fail to reject H0 with either a = .05 or = .01 d. Cannot answer without additional information

b

30. Which of the following will increase the power of a hypothesis test? a. change from .05 to .01 b. change the sample size from 25 to 100 c. change from a one-tailed test to a two-tailed test d. none of these options will increase power

b

37. The advantage of a point estimate compared to an interval estimate is that the point estimate provides a confidence interval. a. true b. false

b

4. As the sample size increases, the standard error also increases a. True b. False c. Not enough information to say d. They stay the same

b

41. Which combination of factors would definitely increase the width of a desired confidence interval? a. use a larger sample and increase desired level of confidence b. use a smaller sample and increase desired level of confidence c. use a larger sample and decrease desired level of confidence d. use a smaller sample and decrease the desired level of confidence

b

5. (From ReviewMaster) The general statement of the null hypothesis for the one-sample tests of Chapter 10 is a. H0: s = a b. H0: μ = a c. H0: t = a d. H0: μ = t

b

5. A sample of n=4 scores comes from a sampling distribution of means with !! = 5. This sample was selected from a population with a standard deviation of σ = 20. a. True b. False: σ = 10 c. False: σ = 30 d. False: σ = 40

b

7. The rejection region is a. the difference between a Type I and a Type II error b. the region beyond the critical value(s) c. the standard error of the sample statistic divided by d. the region between the two standard errors

b

8. For a population with = 80 and σ = 20, the sampling distribution of means based on n=16 will have a mean of _____ and a standard error of _____. a. 5, 80 b. 80, 5 c. 20, 20 d. 80, 1.25

b

38. If a sample of n = 9 scores is used to make a 90% confidence interval estimate of the population mean, then the values of t = ± 2.306 would be used in the equation. a. true b. false: ± 1.860 c. false: ± 1.833 d. need more information

b = becausse n = 9, df = n-1=8, look at t table for df=8 when a= 0.10 for nondirectional 2 tailed test

2. (From ReviewMaster) Which of the following is a measure of effect size? a. z b. s c. d d. t

c

21. By selecting a smaller alpha level, a researcher is _____. a. attempting to make it easier to reject H0 b. better able to detect a treatment effect c. reducing the risk of a Type I error d. all of the above

c

21. The number of degrees of freedom for the one-sample test for the mean when σ is unknown is a. n b. N c. n - 1 d. N - 1 e. not applicable

c

23. If the sample size is increase from n=20 to n=50, what happens to the size of the region of rejection? a. it increases b. it decreases c. the sample size has no influence on the size of the region of rejection

c

24. Assume that for a particular experiment, the null hypothesis is H0: μ = 50, σ is not known, and the test is nondirectional. We collect a sample of size n = 16, and compute the following statistics from the sample data: = 54; s = 8.0; s2 = 64.0 (you may not need to know all these statistics). Then the effect size index d is a. 54 b. 4 c. .5 d. 2.0

c

3. The observed value of a sample statistic is a. the beginning of the rejection region b. what you see in the data prior to performing any computations c. a computed statistic of a sample d. a computed parameter

c

31. If the null hypothesis is H0: μ = 25 and the effect size index d = .5, then we know that a. half the subjects in the sample obtained scores higher than 25 b. half the subjects in the sample obtained scores lower than 25 c. the mean of the sample is half a standard deviation from 25 d. the mean of the sample is half a standard error from 25

c

36. If other factors are held constant, which of the following is a consequence of increasing the sample size? a. an increased standard error and an increased likelihood of rejecting H0 b. an increased standard error and a decreased likelihood of rejecting H0 c. a decreased standard error and an increased likelihood of rejecting H0 d. a decreased standard error and a decreased likelihood of rejecting H0

c

39. Compared to a point estimate, an interval estimate _______. a. has greater precision and greater confidence b. has greater precision but less confidence c. has less precision but greater confidence d. has less precision and less confidence

c

4. (From ReviewMaster) What do the results of a non-directional hypothesis test and a confidence interval centered on an observed mean have in common? a. They are both things that are too complicated for me b. They are both indicators of how much overlap two distributions have c. They contain the same information, and would thus lead to similar conclusions d. They indicate the significance level that should be used in testing future hypotheses

c

9. If other factors are held constant, the mean of the sampling distribution of means will _______ as the same size increases. a. increase b. decrease c. stay constant d. Not enough information to say.

c

10. A sampling distribution with n=4 has a standard error of 10 points. For the same population, what is the standard error of the sampling distribution with n=16? a. 1 b. 2.5 c. 5 d. 10

c look at word doc for this solution

11. A random sample of n=4 scores is selected from a normally distributed population with = 80 and σ = 12. What is the probability that the sample mean will be greater than 86? a. 0.0228 b. 0.066 c. 0.1587 d. 0.3085

c look at word doc for this solution

35. A researcher reports a significant treatment effect with t(24) = +3.04. How many scores were in the sample? a. 23 b. 24 c. 25 d. cannot be determined

c t(24) = t(degrees of freedom) and degrees of freedom = n - 1

1. (From ReviewMaster) What does the subscript 'obs' mean? a. A criterion set in advance that demarcates the beginning of the rejection region b. A computed value, typically of a population parameter c. An observation of the population parameter(s) d. A computed value, typically of a sample or test statistic

d

1. There are three distributions that can be sketched to illustrate a hypothesis testing procedure. These distributions are a. the variable, the square of the variable, and the absolute value of the variable b. the variable, the absolute value of the variable, and the variance of the variable c. the variable, the rejected variable, and the accepted variable d. the variable, the sample statistic, and the test statistic

d

17. The observed value of the test statistic when σ is unknown is a. αobs b. σobs c. zobs d. tobs

d

18. The critical value of the test statistic when σ is unknown is a. αcv b. σcv c. zcv d. tcv

d

25. Assume that for a particular experiment, the null hypothesis is H0: μ = 50, σ is not known, and the test is nondirectional. We collect a sample of size n = 16, and compute the following statistics from the sample data: = 54; s = 8.0; s2 = 64.0 (you may not need to know all these statistics). Then tobs is a. 54 b. 4 c. .5 d. 2.0

d

28. Assume that for a particular experiment, the null hypothesis is H0: μ = 10, σ is known to be 3, and the test is nondirectional. We collect a sample of size n = 9, and compute the following statistics from the sample data: = 12; s = 4.0; s2 = 16.0 (you may not need to know all these statistics). Then the effect size index d is a. 12 b. 2 c. 1.5 d. .667

d

29. Assume that for a particular experiment, the null hypothesis is H0: μ = 10, σ is known to be 3, and the test is nondirectional. We collect a sample of size n = 9, and compute the following statistics from the sample data: = 12; s = 4.0; s2 = 16.0 (you may not need to know all these statistics). Then tobs is a. 12 b. 2.0 c. 1.0 d. not the appropriate test statistic for this study

d

30. Assume that for a particular experiment, the null hypothesis is H0: μ = 10, σ is known to be 3, and the test is nondirectional. We collect a sample of size n = 9, and compute the following statistics from the sample data: = 12; s = 4.0; s2 = 16.0 (you may not need to know all these statistics). The number of degrees of freedom for the test statistic is a. 8 b. 9 c. 10 d. unnecessary in this study

d

6. The mean of a sampling distribution of means with n = 16 equals 50. This sample was selected from a population with a mean of: a. u = 25 b. = 55 c. = 51 d. = 50

d

34. A sample of n = 4 scores has a mean of 35 and!Σ !! − ! !! = 48. What are the values for the sample standard deviation and the estimated standard error for the sample mean? a. s = 16 and sx = 4 b. s = 16 and sx = 2 c. s = 4 and sx = 1 d. s = 4 and sx = 2

d look at word doc for solution

40. A sample of n = 5 scores has a mean of !! = !45 and a variance of s2 = 20. Using this sample, the 95% confidence interval for the population mean is: a. !!" = !45! ± !2.776(20) b. !!" = !45! ± !2.132(2) c. !!" = !45! ± !2.132(20) d. !!" = !!"! ± !!. !!"(!)

d look at word doc for solution

As sample size increases, the standard error

decreases

8. One can show the rejection region on the distribution of the _____________. a. variable b. sample statistic c. test statistic d. both the variable and the sample statistic e. both the sample statistic and the test statistic

e

20. The number degrees of freedom for the one-sample test for the mean when σ is known is a. n b. N c. n - 1 d. N - 1 e. not applicable

e; degrees of freedom are only used when sigma is unknwon

33. To calculate a t statistic, what information is needed? a. the alpha level and b. the value for s or s2 c. the!! (sample mean) and n d. all of the above e. none of the above f. b & c only g. a & c only h. aren't these questions the worst?

f

combination of facts that is most likely to result in you rejecting the Ho

large sample size and a small population of standard deviation

43. You select a sample of n = 36 individuals from a normal population with = 70 and σ = 6. These 36 students undergo meditation training to see if it affects problem solving ability. Following the training, the students obtained a sample mean (!) of 73. 1. Conduct a hypothesis test to find out if the meditation training had a significant effect. Use a two-tailed test with = .05.

look at word doc for solution p10 the z score we obtained lies in the region of rejection, this indicates that the sample mean of X(bar) = 73 is an extreme of unusual value if it did in fact come from a population with a u=70. therefore, our statistical decision is to reject Ho.

As sample size increases, so does the

power of a test

by selecting a smaller alpha level, the researcher is

reducing the risk of type 1 error

a hypothesis test has an alpha of 0.05. if the sample data produce a z-score of -2.24, then what's the correct decision

reject the null and conclude the treatment has an effect

Large variance lowers the likelihood of

rejecting the null hypothesis

the probability that the test will reject H0 if there is a real treatment effect

represented as B, 1-B

in a hypothesis test, the critical region consists of

sample values that are very unlikely to occur if H0 is true

The smaller the alpha, the

smaller the probability

The region of rejection consists of sample means with very low probability of occurring if the null hypothesis is

true

a population has a mean of u=45. if a researcher predicts that the experimental treatment will produce a DECREASE in the scores, the Ho for one=tailed test would state

u greater than and equal to 45

The mean of the sampling distribution of the means is equal to

u independent of n