Exam 14: Testing Hypotheses About the Difference Between Two Independent Groups

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The assumption of homogeneity of variance means that

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Suppose that X and Y stand for scores on a test of learning under conditions of reward and punishment, respectively. If we are interested only in whether reward results in higher scores than punishment, and obtain the difference between the two conditions in terms of Suppose that X and Y stand for scores on a test of learning under conditions of reward and punishment, respectively. If we are interested only in whether reward results in higher scores than punishment, and obtain the difference between the two conditions in terms of    , we should place the region of rejection , we should place the region of rejection

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You read in a popular new magazine "A group of college women scored significantly higher, on the average, than a group of college men on the specially constructed test of intuitive problem solving." (a)How is the statistically unsophisticated person likely to interpret the above statement (consider in particular the italicized phrase)? (b)What does the statement really mean? Answer in terms of what was tested and what was decided. (c)Is it possible that the difference in means between the women and men was in fact quite small? If so, how could a significant difference be observed? (d)What additional statistical information would you want in order to evaluate the difference between the women and the men?

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(a) Difference between the sexes large and "important" 
(b)  (a) Difference between the sexes large and important  (b)     tested and rejected; conclusion:      (c) yes; very large samples would result in a very small standard error and a large t  (d)    and estimates of the population standard deviations (e.g., s<sub>p</sub>).
tested and rejected; conclusion:
(a) Difference between the sexes large and important  (b)     tested and rejected; conclusion:      (c) yes; very large samples would result in a very small standard error and a large t  (d)    and estimates of the population standard deviations (e.g., s<sub>p</sub>).

(c) yes; very large samples would result in a very small standard error and a large t 
(d)  (a) Difference between the sexes large and important  (b)     tested and rejected; conclusion:      (c) yes; very large samples would result in a very small standard error and a large t  (d)    and estimates of the population standard deviations (e.g., s<sub>p</sub>). and estimates of the population standard deviations (e.g., sp).

    The effect size d is The effect size d is

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Suppose that Suppose that    Suppose also that the effect size    Thus,   must equal Suppose also that the effect size Suppose that    Suppose also that the effect size    Thus,   must equal Thus, Suppose that    Suppose also that the effect size    Thus,   must equal must equal

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We wish to compare the marriage counselors from two different clinics with regard to how often couples they have counseled seek a divorce. As many as possible of the couples counseled by each of the counselors are located. The following are the percentages for each counselor of client couples who obtained, or were seeking, a divorce one year after termination of counseling:  We wish to compare the marriage counselors from two different clinics with regard to how often couples they have counseled seek a divorce. As many as possible of the couples counseled by each of the counselors are located. The following are the percentages for each counselor of client couples who obtained, or were seeking, a divorce one year after termination of counseling:    Set up the appropriate statistical hypotheses; perform the test ( \alpha  = .05); and draw final conclusions. Set up the appropriate statistical hypotheses; perform the test ( α\alpha = .05); and draw final conclusions.

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In a two-group experiment, random assignment

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The central limit theorem is of assistance for the sampling distribution of

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The scores from two randomly selected samples from populations A and B are as follows: A: 2, 4,B: 3, 5.The pooled variance estimate, The scores from two randomly selected samples from populations A and B are as follows: A: 2, 4,B: 3, 5.The pooled variance estimate,     would equal would equal

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We are screening drugs for possible use against cancer. We implant 11 laboratory mice with cancer cells. Five of them selected at random are treated with Theron-P. Two months later, detectable tumors are removed from all 11 animals and weighed. The following are the results (in grams):  We are screening drugs for possible use against cancer. We implant 11 laboratory mice with cancer cells. Five of them selected at random are treated with Theron-P. Two months later, detectable tumors are removed from all 11 animals and weighed. The following are the results (in grams):     (a) Set up         and       .  (b)Perform the test ( \alpha  = .05) (c) Draw final conclusions. (a) Set up  We are screening drugs for possible use against cancer. We implant 11 laboratory mice with cancer cells. Five of them selected at random are treated with Theron-P. Two months later, detectable tumors are removed from all 11 animals and weighed. The following are the results (in grams):     (a) Set up         and       .  (b)Perform the test ( \alpha  = .05) (c) Draw final conclusions. and  We are screening drugs for possible use against cancer. We implant 11 laboratory mice with cancer cells. Five of them selected at random are treated with Theron-P. Two months later, detectable tumors are removed from all 11 animals and weighed. The following are the results (in grams):     (a) Set up         and       .  (b)Perform the test ( \alpha  = .05) (c) Draw final conclusions. . (b)Perform the test ( α\alpha = .05) (c) Draw final conclusions.

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We wish to test the hypothesis of no difference between the means of two independent samples. The first sample consists of 30 cases and the second consists of 20 cases. The number of degrees of freedom for the test is

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The makers of Streamer automobiles wish to compare two possible carburetors for use in their larger V-6 model with regard to gasoline consumption. Eight new Streamers with V-6 engines are randomly divided into two groups. One group has Type L carburetors installed and the other, Type M carburetors. The following are the results of standard city mileage tests on the Streamers (in mpg):  The makers of Streamer automobiles wish to compare two possible carburetors for use in their larger V-6 model with regard to gasoline consumption. Eight new Streamers with V-6 engines are randomly divided into two groups. One group has Type L carburetors installed and the other, Type M carburetors. The following are the results of standard city mileage tests on the Streamers (in mpg):    Set up      and    ; perform the test ( \alpha  = .05), and draw final conclusions. Set up  The makers of Streamer automobiles wish to compare two possible carburetors for use in their larger V-6 model with regard to gasoline consumption. Eight new Streamers with V-6 engines are randomly divided into two groups. One group has Type L carburetors installed and the other, Type M carburetors. The following are the results of standard city mileage tests on the Streamers (in mpg):    Set up      and    ; perform the test ( \alpha  = .05), and draw final conclusions. and  The makers of Streamer automobiles wish to compare two possible carburetors for use in their larger V-6 model with regard to gasoline consumption. Eight new Streamers with V-6 engines are randomly divided into two groups. One group has Type L carburetors installed and the other, Type M carburetors. The following are the results of standard city mileage tests on the Streamers (in mpg):    Set up      and    ; perform the test ( \alpha  = .05), and draw final conclusions. ; perform the test ( α\alpha = .05), and draw final conclusions.

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The exact nature of the random sampling distribution of differences between two means is dependent on

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To test the null hypothesis of no difference between two means, we calculate the statistic

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The variance estimate made by pooling data from two samples is calculated by

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The test of the difference between two means involves comparison of means of

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As used in most behavioral science experiments, statistical inference procedures do not provide us with

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You plan to perform an experiment and conduct a two-tailed test of  You plan to perform an experiment and conduct a two-tailed test of     ( \alpha  = .05).  Suppose that in fact    How many times out of 100 repetitions of your experiments would you expect to obtain significant results if you use samples of size: (a)8(b) 15 (c)45(d)110 ( α\alpha = .05). Suppose that in fact  You plan to perform an experiment and conduct a two-tailed test of     ( \alpha  = .05).  Suppose that in fact    How many times out of 100 repetitions of your experiments would you expect to obtain significant results if you use samples of size: (a)8(b) 15 (c)45(d)110 How many times out of 100 repetitions of your experiments would you expect to obtain significant results if you use samples of size: (a)8(b) 15 (c)45(d)110

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In testing the difference between two means, the total of sample size is, in general, used most efficiently when

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If some fact of an experiment results in a smaller standard error of the difference between two means than otherwise, this is

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