Module 9 Flashcards
The region of rejection typically appears \_\_\_\_\_ of the sampling distribution? A) Above the mean B) Below the mean C) In the Center D) At the extremes
D) At the extremes
If the sample mean is of the kind that could readily occur when the null hypothesis is true, we will A) Reject H₀ B) Retain H₀ C) Suspend judgment D) Change the level of significance
B) Retain H₀
The criterion by which a decision is made about the null hypothesis is called A) The level of significance B) Alpha C) Either of the above D) The alternative hypothesis
C) Either of the above
According to the information contained in the sampling distribution, we reject the null hypothesis if the probability of obtaining such a sample mean is A) Known B) Estimated C) Low D) High
C) Low
The null hypothesis is always A) Specific B) Retained for deviant sample results C) The hypothesis of no difference D) (A) and (B) above
A) Specific
Assume σ is known. What are the critical values for testing H₀: μ = 200 against H₁: μ ≠ 200 with α = .04? A) ±1.75 B) ±1.41 C) ±2.05 D) ±1.67
C) ±2.05
Assume σ is unknown. What are the critical values for testing
H₀: μ = 60 against H₁: μ ≠ 60 with α = .08?
A) ±1.75
B) ±1.41
C) ±2.05
D) ±1.67
A) ±1.75
In order to test H₀, we must assume
A) A normal distribution shape
B) It is true
C) A level of significance of 0.05 or 0.01
D) Representative sample results (except for sampling error)
B) It is true
When the value of α is changed from 0.05 to 0.01,
A) The greater the desireability of using a two-tailed test
B) The greater the value of z required to reject the null hypothesis
C) The smaller the region of retention
D) We should be less confident about our decision if that decision is to reject the null hypothesis
B) The greater the value of z required to reject the null hypothesis
In testing a hypothesis about the population mean, the sample mean is compared with
A) Sample means that would occur when the hypothesis is false
B) Sample means that would occur when the hypothesis is true
C) Various population means that could occur
D) Means of samples for all possible values of n
B) Sample means that would occur when the hypothesis is true
The statistical hypothesis to be tested is called the A) Trial hypothesis B) Directional hypothesis C) Alternative hypothesis D) Null hypothesis
D) Null hypothesis
In testing a hypothesis about a mean, the mean of the sampling distribution is taken to be A) The value stated in H₀ B) The value stated in H₁ C) Either (A) or (B) D) Neither (A) nor (B)
A) The value stated in H₀
When the value of α is changed from 0.05 to 0.01:
A) The standard error of the mean is reduced.
B) The significance level is lowered.
C) The more deviant a sample mean must be before it leads to rejection of the null hypothesis.
D) Both (b) and (c).
D) Both (b) and (c)
If the outcome of a test is significant at the .01 level, it
A) Also will be significant at the 0.05 level
B) Will not be significant at the 0.05 level
C) May be significant at the 0.05 level
D) Probably will not be significant at the 0.05 level
A) Also will be significant at the 0.05 level
The assertion of statistical significance
A) Means that H₀ could well be true
B) Indicates all other hypotheses have been eliminated
C) Is meaningful only in connection with the level of significance used
D) Indicates the statistical importance of the results
C) Is meaningful only in connection with the level of significance used
Given: x̄ = 102, H₀: μ = 100, H₁: μ ≠ 100. If H₀ is retained, this means that
A) No other H₀ could be true
B) Other null hypotheses are probably not true
C) H₀ is probably true
D) H₀ could be true, but so could other null hypotheses
H₀ could be true, but so could other null hypotheses
Statistical significance means
A) Rejection of H₁
B) A significant finding, after the statistical analysis
C) An important difference between the hypothesized and the population value
D) Rejection of H₀
D) Rejection of H₀
The choice between a one-tailed test and a two-tailed test
A) Will affect the way H₀ is stated
B) Should be made after learning the location of x̄
C) Is determined by the logic of the study rather than by the outcome of the data
D) Is a matter of taste; some statisticians prefer (B) and some prefer (C)
C) Is determined by the logic of the study rather than by the outcome of the data
“One-tailed” is to “two-tailed” as: A) “Significant” is to “nonsignificant” B) “p” is to “α” C) “H₀” is to “H₁” D) “Directional” is to “nondirectional”
D) “Directional” is to “nondirectional”
Assume that H₁: μ < μ₀. The statistical decision following from “p > α” is identical to that following from A) z > -zₐ B) x̄ > μ₀ C) z > -zₐ D) None of the above
A) z > -zₐ
Which, if any, need not be decided in advance of conducting the test of a null hypothesis? A) The level of significance B) The nature of H₁ C) The region of rejection D) All should be decided in advance
D) All should be decided in advance
If we test H₀: μ = 100 against H₁: μ < 100, the region of rejection will be located A) At the extreme right B) At the extreme left C) At the two extremes D) In the center
B) At the extreme left
We originally plan to use a two-tailed test but then change our mind (before collecting our data) and move to a one-tailed test. For the one-tailed test
A) The critical value will be numerically less
B) The critical value will be numerically greater
C) The value of α will be exactly half that for the two-tailed test
D) The null hypothesis will be stated differently
A) The critical value will be numerically less
For a one-tailed test (α is known), the critical values for testing a hypothesis about μ at α = .05 and α = .01 are, respectively A) 1.58 and 2.96. B) 1.65 and 2.33. C) 1.96 and 2.58. D) 1.33 and 2.64.
B) 1.65 and 2.33
For a two-tailed test (α is known), the critical values for testing a hypothesis about μ at α = .05 and α = .01 are, respectively A) 1.58 and 2.96. B) 1.65 and 2.33. C) 1.96 and 2.58. D) 1.33 and 2.64.
C) 1.96 and 2.58
Which of the following is true?
A) α specifies the size of the region of rejection, and H₀ specifies where it is to be located
B) α specifies the nature of the alternative hypothesis, and H₁ specifies where the region of rejection is to be located
C) α specifies the size of the region of rejection, and H₁ specifies where it is to be located
D) α specifies the probability of coming to a wrong conclusion when the hypothesis is false, and H₀ specifies where the region of rejection is to be located
C) α specifies the size of the region of rejection, and H₁ specifies where it is to be located
The region of rejection is determined by A) The level of significance B) The nature of the alternative hypothesis C) Both (a) and (b) D) Neither (a) nor (b)
C) Both (a) and (b)
We never assume the H₁ to be true in order to test it, because A) It is a "dummy" hypothesis B) It is not specific C) Our primary concern is with the H₀ D) All of the above
B) It is not specific
“H₀” is to “H₁” as: A) “Specific” is to “nonspecific” B) “Specified in advance” is to “specified later” C) “True” is to “false” D) “Retain” is to “reject”
A) “Specific” is to “nonspecific”
Which of the first three statements, if any, is false? H₀ is:
A) The hypothesis about which the statistical decision is made
B) Always a statement about a parameter
C) Always expressed as a point value
D) None of the above is true
D) None of the above is true
We expect the alternative hypothesis to be a: A) Particular value of a statistic B) Range of values for a statistic C) Particular value of a parameter D) Range of values for a parameter
D) Range of values for a parameter
Which of the first three statements, if any, is false? H₁ is:
A) Always a statement about a parameter
B) Expressed as a range of values
C) States whether the test is directional or nondirectional
D) None of the above is false
D) None of the above is false
Which of the following has the characteristic form of a null hypothesis? A) μ > 150 B) μ ≠ 150 C) μ = 150 D) All of the above
C) μ = 150
A type I error is committed when a: A) True null hypothesis is rejected B) False null hypothesis is retained C) True alternative hypothesis is retained D) α is higher than it should be
A) True null hypothesis is rejected
The smaller the level of significance
A) The less the probability of a Type I error
B) The less the probability of a Type II error
C) The greater the probability of a Type I error
D) The less confident we may be in whatever statistical conclusion is reached
A) The less the probability of a Type I error
Which of the following will increase the probability of making a type II error?
A) Use α = .01 rather than .05
B) Use dependent samples
C) Increase n
D) Use a one-tailed test (correct direction)
A) Use α = .01 rather than .05
When α is assigned a very small value:
A) We can be more certain of our conclusions, whatever the circumstances
B) There is a greater risk of rejecting the hypothesis when it is true
C) We should use a two-tail test
D) We may overlook a real difference between μ and
μ₀ more easily than otherwise
D) We may overlook a real difference between μ and μ₀ more easily than otherwise
A type II error is committed when a: A) True null hypothesis is rejected B) False null hypothesis is retained C) True alternative hypothesis is retained D) α is higher than it should be
B) False hypothesis is retained
When α is assigned a relatively large value:
A) We can be more certain of our conclusions, whatever the circumstances
B) There is a greater risk of rejecting the hypothesis when it is true
C) We should use a two-tail test
D) We may overlook a real difference between μ and
μ₀ more easily than otherwise
B) There is a greater risk of rejecting the null hypothesis when it is true
When the value of α is changed from .05 to .01:
A) The region of rejection becomes smaller
B) The lower the probability of rejecting H0 when it is true
C) Both of the above are true
D) The larger n should be
C) Both of the above are true
If α = .05, the null hypothesis will be:
A) Rejected 5% of the time
B) Rejected 5% of the time when it is true
C) Retained 5% of the time
D) Retained 5% of the time when it is true
B) Rejected 5% of the time when it is true
When we use the 0.05 level of significance,:
A) We will be right 5% of the time
B) We will be wrong 5% of the time
C) We will reject true hypotheses 5% of the time
D) We will accept false hypotheses 5% of the time
C) We will reject true hypotheses 5% of the time
Which of the following is a hypothesis testing rather than an estimation question?
A) What is the proportion of psychology majors going on to graduate school?
B) How tall is the average 1st grader?
C) Does the new teaching method result in greater learning compared with the old?
D) None of the above
C) Does the new teaching method result in greater learning compared with the old?
Which of the following is an estimation rather than a hypothesis testing question?
A) Are this year’s 1st graders taller, on the average, than those 10 years ago?
B) Does the mean score for the applicant population differ from the national norm?
C) How much of an effect does the drug have on fine motor coordination?
D) None of the above
C) How much of an effect does the drug have on fine motor coordination?
Which statement is true?
A) Any problem in hypothesis testing could be handled through estimation
B) Any problem in estimation could be handled through hypothesis testing
C) Hypothesis testing and estimation are mutually interchangeable
D) Hypothesis testing and estimation are never interchangeable
A) Any problem in hypothesis testing could be handled through estimation
Estimation of a parameter (i.e., population value such as ∞) is particularly indicated over hypothesis testing when:
A) Great accuracy is required
B) Logic does not point to a possible value of the parameter that is of special interest
C) We know the parameter’s value and wish to predict sample outcomes
D) Sampling is not random
B) Logic does not point to a possible value of the parameter that is of special interest
Interval estimates are generally to be preferred over point estimates because interval estimates: A) Have a firmer statistical basis B) Result in greater precision C) Account for a sampling error D) Are based on more degrees of freedom
C) Account for a sampling error
Point estimates alone have serious limitations because of
A) Statistical bias
B) Difficulties in coming up with an exact value
C) Random sampling variation
D) The hypothetical nature of confidence limits
C) Random sampling variation
From a random sample of 20 cases, we estimate μ to equal 23.4. This is an example of A) Point estimation B) Exact estimation C) Random estimation D) Interval estimation
A) Point estimation
The rule for constructing an interval estimate of the population mean is A) μ ± zα σx̄ B) z ± x̄σx̄ C) x̄ ± zα σ D) x̄ ± zα σx̄
D) x̄ ± zα σx̄
Which statement is incorrect?
A) Interval estimates are preferred over point estimates because they are more likely to be correct
B) The population value to be estimated does not vary, but estimates made from different samples will vary
C) Once an interval estimate is constructed, it is no longer proper to speak of the probability that it includes the population value
D) None of the above
D) None of the above
For a random sample of 100 cases, x̄ = 150 (σ = 35). The 95% confidence interval for μ would run approximately from A) 143 to 157 B) 131 to 169 C) 147 to 153 D) 138 to 162
A) 143 to 157
Procedures not covered in the text are used to construct a 90% confidence interval for P, the population proportion of freshmen able to pass a proposed English placement exam. The sample interval runs from 0.43 to 0.49. This tells us that:
A) There is a 90% probability that P falls between 0.43 and 0.49
B) There is a 90% probability that an interval so constructed will include P
C) 90% of the time P will fall between 0.43 and 0.49
D) 90% of the intervals so constructed will fall between 0.43 and 0.49
B) There is a 90% probability that an interval so constructed will include P
A 99% confidence interval is constructed for μ and runs from 46.7 to 55.6. The 99% refers to
A) The probability that μ falls between 46.7 and 55.6
B) The percent of successive samples that will have means between 46.7 and 55.6
C) The proportion of times the interval 46.7 and 55.6 will include μ
D) None of the above
D) None of the above
Which set of circumstances is most likely to result in a narrow confidence interval?
A) Large n and a confidence level of 0.95
B) Large n and a confidence level of 0.99
C) Small n and a confidence level of 0.95
D) Small n and a confidence level of 0.99
A) Large n and a confidence level of 0.95
For an interval estimate of μ, an estimate of lesser width results
A) When n is smaller
B) When σ is larger
C) When a higher level of confidence is used
D) None of the above
D) None of the above
Suppose a 95% confidence interval for μ runs from 48 to 56. If we had tested H₀: μ = 49 against H₁: μ ≠ 49 using α = .05, we would:
A) Have rejected H₀
B) Have retained H₀
C) Not be able to decide about H₀ unless n were known
D) Not be able to decide about H₀ unless σ were known
B) Have retained H₀
When the population standard deviation is unknown, the standard error of the mean may be estimated by: A) s/√(n) B) s/√(n-1) C) Either of the above D) Neither of the above
A) s/√(n)
For inference about means, we need to know the value of the standard deviation of the population. We estimate its value by calculating A) √(SS/(n)) B) √(SS/(n-1)) C) Either of the above D) Neither of the above
B) √(SS/(n-1))
Consider the following sample of three scores: 2, 4, and 6. The best estimate of the population standard deviation is: A) 2 B) √2.67 C) 4 D) √8
A) 2
For the following sample of two scores, 1 and 3, the best estimate of the population standard deviation is A) 10 B) 1 C) 1.414 D) 1.732
C) 1.414
Consider the following sample of three scores: 1, 3, and 5. The best estimate of the standard error of the mean is A) 1.15 B) 1.73 C) 2.27 D) 2.52
A) 1.15
For a sample of 16 cases, the best estimate of the population standard deviation is calculated to be 8.36. The best estimate of the standard error of the mean (for samples of size 16) is A) 2.16 B) 0.522 C) 2.09 D) 4.18
C) 2.09
When testing a hypothesis about μ, critical values obtained from the normal curve table are not, strictly speaking, correct because
A) H₀ is usually false
B) We must estimate the value of σ
C) The distribution of our sample results usually departs from normality
D) The sampling distribution of means only approaches normality; it never actually reaches normality
B) We must estimate the value of σ
Which sets of values will allow us to calculate the t required to test a hypothesis about a mean? A) n, sx̄ , μ₀ B) s, x̄ , μ₀ C) n, s, x̄ , μ₀ D) s, σ, x̄ , μ₀
C) n, s, x̄ , μ₀
The t distribution is designed to correct for errors introduced when
A) The population standard deviation is estimated from the sample
B) Sampling is not random
C) Sampling is without replacement
D) The distribution of sample means is skewed
A) The population standard deviation is estimated from the sample
In general, “degrees of freedom” is most clearly related to the A) Level of significance B) Value of x̄ C) Value of sx̄ D) Sample size
D) Sample size
Which of the following most readily “explains” the df associated with s?
A) There are n – 1 opportunities for s to vary
B) ∑(X - x̄) = 0
C) Squaring the deviation scores makes them all positive
D) There are n – 1 opportunities for x̄ to vary
B) ∑(X - x̄) = 0
Basically, “degrees of freedom” refers to
A) The amount of freedom x̄ has to vary
B) Independent pieces of information
C) Alternatives we have in analyzing data
D) Freedom for n to vary
B) Independent pieces of information
When the number of degrees of freedom is very large,
A) t will be essentially equal to the true z
B) s will be very close to σ
C) sx will be very close to σ
D) All of the above
D) All of the above
As the number of degrees of freedom increases, Student’s distribution
A) Remains the same
B) Changes slowly at first, then more rapidly
C) Changes rapidly at first, then more slowly
D) Changes at an even rate
C) Changes rapidly at first, then more slowly
We conduct a two-tailed test at the α = .05 with data that afford 75 degrees of freedom. When we look up the critical value of t, we will expect it to be \_\_\_\_\_ the corresponding critical value of z from the normal curve table. A) Substantially larger than B) A little larger than C) A little smaller than D) Substantially smaller than
B) A little larger than
As the number of degrees of freedom changes, the t distribution A) Remains the same B) Varies in its mean C) Varies in its shape D) Varies in its degree of symmetry
C) Varies in its shape
The distribution of t
A) Has more area in its tails than does the normal distribution of z
B) Varies in shape
C) Depends on the number of degrees of freedom
D) All of the above
D) All of the above
The standard deviation of the distribution of t is
A) Larger than the standard deviation of the true z
B) The same as the standard deviation of the true z
C) Smaller than the standard deviation of the true z
D) Sx
A) Larger than the standard deviation of the true z
We are testing H₀: μ = 50 against H₁: μ < 50 using a sample of 7 cases. The critical value of t for α = .01 is A) -2.998 B) -3.499 C) -3.143 D) -3.707
C) -3.143
We are testing H₀: μ = 100 against H₁: μ ≠ 100 using a sample size of 10. The critical value of t for α = .02 is A) 2.764 B) 2.821 C) 2.262 D) 1.812
B) 2.821
We are testing H₀: μ = 100 against H₁: μ ≠ 100 using a sample size of 15. The critical value of t for α = .10 is A) 1.761 B) 1.345 C) 1.753 D) 1.746
A) 1.761
We conduct a two-tailed test at α = .05 with data that afford 4 degrees of freedom. When we look up the critical value of t, we will expect it to be \_\_\_\_\_ the corresponding critical value of z from the normal curve table. A) Substantially larger than B) A little larger than C) A little smaller than D) Substantially smaller than
A) Substantially larger than
The mean of the t distribution: A) Is equal to the value specific in H₀ B) Is unknown but a constant C) Is zero D) Depends on the df
C) Is zero
Which statement is false? The t distribution and the normal distribution of z are alike in that both A) Are symmetrical B) Have the same standard deviation C) Have the same mean D) Are unimodal
B) Have the same standard deviation
When small samples are selected from a normal population:
A) The value of x̄ tends to be too large
B) The sampling distribution of means follows Student’s t distribution
C) The value of s tends to be too small
D) None of the above
D) None of the above
If the sample consists of 6 scores, the calculated value of t does not follow Student’s t distribution when
A) The population standard deviation is unknown
B) A non-normal population has been sampled
C) The alternative hypothesis is nondirectional
D) None of the above
B) A non-normal population has been sampled
The p value:
A) Is based on the assumption that H₀ is true
B) Is an alternative way of reporting the level of significance
C) Is the probability that H₀ is true
D) Is rarely reported
A) Is based on the assumption that H₀ is true
Professor Davis reports: “My results were not significant at the .10 level.” From this we can infer that
A) Professor Davis used α = 0.10 and rejected H₀
B) Professor Davis used α = 0.10 and retained H₀
C) p > 0.10
D) p = 0.10
C) p > 0.10
“p value” is to “level of significance” as
A) “Retention” is to “rejection”
B) “Sample value” is to “criterion”
C) “Rare” is to “typical”
D) “Probability” is to “decimal fraction”
B) “Sample value” is to “criterion”
Which of the following expresses the relationship between level of significance and p value?
A) They are essentially the same thing
B) One is the standard against which the other is evaluated
C) The p value is normally larger than the level of significance
D) None of the above
B) One is the standard against which the other is evaluated
Given: H₀: μ = 80, H₁: μ > 80, n = 8, α = .05, t = +3.02. p would most likely be reported as A) p > .005. B) p < .02. C) p < .10. D) p < .01.
D) p < .01
Given: H₀: μ = 100, H₁: μ ≠ 100, n = 13, α = .05, t = -2.06. p would most likely be reported as A) p < .15. B) p > .05. C) p > .01. D) p > .025.
B) p > .05
When σ is not known, the rule for constructing an interval estimate of the population mean is: A) x̄ ± tαsx̄ B) tα ± x̄sx̄ C) x̄ ± tασx̄ D) μ ± tαsx̄
A) x̄ ± tαsx̄
Imagine that you construct the 95% confidence interval, 24.50 – 32.50. Which statement below is correct?
A) If H₀: μ = 33 were tested at the .01 level (two-tailed), it would be rejected
B) If H₀: μ = 56 were tested at the .05 level (two-tailed), it would be retained
C) If H₀: μ = 14 were tested at the .05 level (two-tailed), it would be rejected
D) If H₀: μ = 25 were tested at the .05 level (one-tailed), it would be retained
C) If H₀: μ = 14 were tested at the .05 level (two-tailed), it would be rejected
