Q&A Hero

Q: 15+ If the critical value of t associated with the above formula is 2.12, what would you conclude about your means? a) There is a significant difference between the means. b) There is a significant difference between the standard deviations. c) There is no significant difference between the means. d) p > .05

Q: 14+ In the formula for t, 1.73 is a) the standard deviation of the sample. b) the standard deviation of the population. c) the standard error of the mean. d) the difference between the means.

Q: 13+ In the formula for t, there are _______ pairs of observations in the study. a) 17 b) 34 c) 18 d) 4.18

Q: 12+ At test, in general, involves a) dividing the difference between means by the standard deviation of the population. b) dividing the difference between means by the standard deviation of the sample. c) dividing the difference between means by the standard error of a distribution of differences between means. d) dividing the difference in standard deviations by the size of the larger mean.

Q: 11+ The null hypothesis in a repeated measures t test is a) the hypothesis that the mean difference score is equal to 0. b) the hypothesis that the mean difference score is different from 0 in either direction. c) the hypothesis that post scores are larger than pre-scores. d) the hypothesis that the variance of scores stays constant from pretest to posttest.

Q: 10+ A repeated measures t test is more likely to lead to rejection of the null hypothesis if a) subjects show considerable variability in their change scores. b) many subjects show no change. c) some subjects change a lot more than others. d) the degree of change is consistent across subjects.

Q: 9 If we test the mean amount that alcoholic subjects drink before and after therapy, and that difference is NOT statistically significant, this could mean a) the therapy was not effective. b) the sample size was too large. c) the study lacked sufficient power. d) a and c

Q: 8 We are evaluating a method of therapy for extremely underweight adolescent girls. If we weighed our subjects at the beginning and end of therapy, a difference in weight could mean a) that our therapy worked. b) that people gain weight over time regardless of what we do. c) that our scales changed due to repeated use. d) all of the above

Q: 7 The mean of a column of difference scores is equal to a) the ratio of the means of the individual columns. b) the difference between the means of the individual columns. c) the sample size. d) We can"t tell without calculating it for a set of data.

Q: 6 A difference score is obtained by a) subtracting the Before score from the After score. b) subtracting the After score from the Before score. c) dividing After scores by Before scores. d) either a or b, just so long as you are consistent

Q: 5 We would be least likely to use a repeated measures design when a) there are substantial individual differences. b) there are minimal individual differences. c) we want to control for differences among subjects. d) we want to compare husbands and wives on their levels of marriage satisfaction.

Q: 4 In the preceding question on autonomy in children, we would be most likely to use that design, rather than random sampling of children, because a) we want to control for differences in means. b) we want to control for differences in parenting style. c) we expect scores of children in the same family to be unrelated. d) we want to control for differences in age between first and second born children.

Q: 3+ We want to study the mean difference in autonomy between first-born and second-born children. Instead of taking a random sample of children we take a random sample of families and sort the children into first- and second-born. The dependent variable is a measure of autonomy. This experiment would most likely employ a) a repeated measures analysis. b) an independent measures analysis. c) a correlation coefficient. d) a scatterplot.

Q: 2 We treat the repeated sample case differently from the case involving two separate samples because of a) the difference in the means of the two samples. b) the fact that different subjects were involved. c) the correlation between the two sets of data. d) the size of the sample.

Q: 1 Which of the following terms does NOT belong with the rest? a) related samples b) repeated samples c) independent samples d) matched samples

Q: 68 Briefly describe two factors that affect the magnitude of t.

Q: 67 Explain the following statement: p (100­110) = .90.

Q: 66 In the previous question, what would be the minimum mean score of the teacher's students that would yield a statistically significant difference using a one-tailed test?

Q: 65 The average SAT score for a local high school was 1100. One teacher is convinced that the 25 students who were in his homeroom performed better than the average student in the high school. Their average score was 1125 with a standard deviation of 100. a) Calculate t. b) Evaluate the teacher's "hypothesis" in light of t.

Q: 64 The mean anxiety score in elementary school children is 14.55. A researcher wants to know if children of anxious parents are more anxious than the average child. Below are the anxiety scores from 10 children of anxious parents. 13 14 14 15 15 15 16 17 17 18 a) Calculate the t value. b) Write a sentence to answer the researcher's question.

Q: 63 The following 10 numbers were drawn from a population. 5 7 7 10 10 10 11 12 12 13 a) Calculate the 95% confidence interval for the population mean. b) Is it likely that these numbers came from a population with a mean of 13? Explain.

Q: 62 Calculate the 95% confidence interval for ­ given s = 25, and N = 101.

Q: 61 Given ­ = 100, s = 27, and N = 30:a) Calculate t.b) Write a sentence interpreting the value of t as a two-tailed test.c) Write a sentence interpreting the value of t as a one-tailed test.

Q: 60 Given a sample size of 30, and one sample t = -2.5, what would you conclude about the sample from which the mean was drawn?

Q: 59 Assuming a two-tailed one sample test is being used, what are the critical values for t given the following sample sizes: a) N = 10 b) N = 15 c) N = 30

Q: 58 The larger the difference between the sample mean and the population mean, the larger the t value.

Q: 57 As the sample variability increases, the magnitude of t increases.

Q: 56 When comparing the mean of a sample of 30 people to the population mean, the degrees of freedom are 31.

Q: 55 Student'st distribution essentially accounts for the fact that t is often larger than the corresponding z because it is based on estimated variance, which is biased.

Q: 54 t-tests are used to test a sample mean when the population mean is unknown.

Q: 53 When the population standard deviation is known, z scores are appropriate to test a sample mean.

Q: 52 The standard deviation of a sampling distribution is known as the standard error.

Q: 51 A normal distribution is one in which all outcomes are equally likely.

Q: 50 A sampling distribution of the mean is typically the mean of one sample.

Q: 49 According to the Central Limit Theorem, as the number of samples increases, the distribution will approach the normal distribution.

Q: 48+ The term "effect size" refers to a) how large the resulting t statistic is. b) the size of the p value, or probability associated with that t. c) the actual magnitude of the mean or difference between means. d) the value of the null hypothesis.

Q: 47 The confidence intervals for two separate samples would be expected to differ because a) the sample means differ. b) the sample standard deviations differ. c) the sample sizes differ. d) all of the above

Q: 46 Thet distribution a) is smoother than the normal distribution. b) is quite different from the normal distribution. c) approaches the normal distribution as its degrees of freedom increase. d) is necessary when we know the population standard deviation.

Q: 45 If we compute a confidence interval as 12.65 25.65, then we can conclude thata) the probability is .95 that the true mean falls between 12.65 and 25.65.b) 95% of the intervals we calculate will bracket c) the population mean is greater than 12.65.d) the sample mean is a very precise estimate of the population mean.

Q: 44 A confidence interval computed for the mean of a single sample a) defines clearly where the population mean falls. b) is not as good as a test of some hypothesis. c) does not help us decide if there is a significant effect. d) is associated with a probability statement about the location of a population mean.

Q: 43 When would you NOT use a standardized measure of effect size? a) when the difference in means is itself meaningful b) when it is clearer to the reader to talk about a percentage c) when some other measure conveys more useful information d) all of the above

Q: 42 When you have a single sample and want to compute an effect size measure, the most appropriate denominator is a) the variance of the sample. b) the standard deviation of the sample. c) the sample size. d) none of the above

Q: 41+ The point of calculating effect size measures is to a) decide if something is statistically significant. b) convey useful information to the reader about what you found. c) reject the null hypothesis. d) prove causality.

Q: 40+ Cohen's is an example of a) a measure of correlation. b) an r-family measure. c) a d-family measure. d) a correlational measure.

Q: 39 When are we most likely to expect larger differences between group means? a) when there is considerable variability within groups b) when there is very little variability within groups c) when we have large samples d) when we have a lot of power

Q: 38 At test is most often used to a) compare two means. b) compare the standard deviations of two samples. c) compare many means. d) none of the above

Q: 37 Which of the following statements is true? a) Confidence intervals are the boundaries of confidence limits. b) Confidence intervals always enclose the population mean. c) Sample size does not affect the calculation of t. d) Confidence limits are the boundaries of confidence intervals.

Q: 36 A one-sample t test was used to see if a college ski team skied faster than the population of skiers at a popular ski resort. The resulting statistic was t.05(23) = -7.13, p < .05. What should we conclude? a) The sample mean of the college skiers was significantly different from the population mean. b) The sample mean of the college skiers was not significantly different from the population mean. c) The null hypothesis was true. d) The sample mean was greater than the population mean.

Q: 35+ All of the following increase the magnitude of the t statistic and/or the likelihood of rejecting H0 EXCEPTa) a greater difference between the sample mean and the population mean.b) an increase in sample size.c) a decrease in sample variance.d) a smaller significance level ().

Q: 34+ Which of the following statistics comparing a sample mean to a population mean is most likely to be significant if you used a two-tailed test? a) t = 10.6 b) t = 0.9 c) t = -10.6 d) both a and c

Q: 33 If we fail to reject the null hypothesis in a t test we can conclude a) that the null hypothesis is false. b) that the null hypothesis is true. c) that the alternative hypothesis is false. d) that we don"t have enough evidence to reject the null hypothesis.

Q: 32 The two-tailed p value that a statistical program produces refers to a) the value of t. b) the probability of getting at least that large a value of t if the null hypothesis is false. c) the probability of getting at least that large an absolute value of t if the null hypothesis is true. d) the probability that the null hypothesis is true.

Q: 31+ If we have calculated a confidence interval and we find that it does NOT include the population mean, a) we must have done something wrong in collecting data. b) our interval was too wide. c) we made a mistake in calculation. d) this will happen a fixed percentage of the time.

Q: 30 A 95% confidence interval is going to be _______ a 99% confidence interval. a) narrower than b) wider than c) the same width as d) more accurate than

Q: 29 When we take a single sample mean as an estimate of the value of a population mean, we have a) a point estimate. b) an interval estimate. c) a population estimate. d) a parameter.

Q: 28 If we compute 95% confidence limits on the mean as 112.5 - 118.4, we can conclude thata) the probability is .95 that the sample mean lies between 112.5 and 118.4.b) the probability is .05 that the population mean lies between 112.5 and 118.4.c) an interval computed in this way has a probability of .95 of bracketing the population mean.d) the population mean is not less than 112.5.

Q: 27 Which of the following does NOT directly affect the magnitude of t?a) The actual obtained difference .b) The magnitude of the sample variance (s2).c) The sample size (N).d) The population variance (2).

Q: 26+ If we have run a t test with 35 observations and have found at of 3.60, which is significant at the .05 level, we would write a) t(35) = 3.60, p <.05. b) t(34) = 3.60, p >.05. c) t(34) = 3.60, p <.05. d) t(35) = 3.60, p <05.

Q: 25+ With a one-sample t test, the value of t is a) always positive. b) positive if the sample mean is too small. c) negative whenever the sample standard deviation is negative. d) positive if the sample mean is larger than the hypothesized population mean.

Q: 24+ For a t test with one sample we a) lose one degree of freedom because we have a sample. b) lose one degree of freedom because we estimate the population mean. c) lose two degrees of freedom because of the mean and the standard deviation. d) have N degrees of freedom.

Q: 23 The sampling distribution of the variance is a) positively skewed. b) negatively skewed. c) normal. d) rectangular.

Q: 22+ The variance of an individual sample is more likely than not to be a) larger than the corresponding population variance. b) smaller than the corresponding population variance. c) the same as the population variance. d) less than the population mean.

Q: 21 The reason why we need to solve for t instead of z in some situations relates to a) the sampling distribution of the mean. b) the sampling distribution of the sample size. c) the sampling distribution of the variance. d) the size of our sample mean.

Q: 20 The importance of the underlying assumption of normality behind a one-sample means test a) depends on how fussy you are. b) depends on the sample size. c) depends on whether you are solving for t or z. d) doesn"t depend on anything.

Q: 19 An assumption behind the use of a one-sample t test is that a) the population is normally distributed. b) the sample is normally distributed. c) the population variance is normally distributed. d) the population variance is known.

Q: 18 In using a z test for testing a sample mean against a hypothesized population mean, the formula for z is a) b) c) d) none of the above

Q: 17 When you are using a one-sample t test, the degrees of freedom area) N.b) N - 1.c) N + 1.d) N - 2.

Q: 16 Many textbooks (though not this one) advocate testing the mean of a sample against a hypothesized population mean by using z even if the population standard deviation is not known, so long as the sample size exceeds 30. Those books recommend this because a) they don"t know any better. b) there are not tables for t for more than 30 degrees of freedom. c) the difference between t and z is small for that many cases. d) t and z are exactly the same for that many cases.

Q: 15+ If the standard deviation of the population is 15 and we repeatedly draw samples of 25 observations each, the resulting sample means will have a standard error of a) 2 b) 3 c) 15 d) 0.60

Q: 14+ Suppose that we know that the sample mean is 18 and the population standard deviation is 3. We want to test the null hypothesis that the population mean is 20. In this situation we woulda) reject the null hypothesis at = .05.b) reject the null hypothesis at = .01c) retain the null hypothesis.d) We cannot solve this problem without knowing the sample size.

Q: 13 It makes a difference whether or not we know the population variance because a) we cannot deal with situations in which the population variance is not known. b) we have to call the result t if the population variance is used. c) we have to call the result z if the population variance is not used. d) we have to call the result t if the sample variance is used.

Q: 12 If the population from which we draw samples is "rectangular," then the sampling distribution of the mean will be a) rectangular. b) normal. c) bimodal. d) more normal than the population.

Q: 11 The standard error of the mean is a function of a) the number of samples. b) the size of the samples. c) the standard deviation of the population. d) both b and c

Q: 10 The standard error of the mean is a) equal to the standard deviation of the population. b) larger than the standard deviation of the population. c) the standard deviation of the sampling distribution of the mean. d) none of the above

Q: 9+ If we knew the population mean and variance, we would expect a) the sample mean would closely approximate the population mean. b) the sample mean would differ from the population mean by no less than 1.96 standard deviations only 5% of the time. c) the sample mean would differ from the population mean by no more than 1.64 standard deviations only 5% of the time. d) the sample mean would differ from the population mean by more than 1.96 standard errors only 5% of the time.

Q: 8 With large samples and a small population variance, the sample means usually a) will be close to the population mean. b) will slightly underestimate the population mean. c) will slightly overestimate the population mean. d) will equal the population mean.

Q: 7 If the population from which we sample is normal, the sampling distribution of the mean a) will approach normal for large sample sizes. b) will be slightly positively skewed. c) will be normal. d) will be normal only for small samples.

Q: 6+ Which of the following is NOT part of the Central Limit Theorem? a) The mean of the sampling distribution approaches the population mean. b) The variance of the sampling distribution approaches the population variance divided by the sample size. c) The sampling distribution will approach a normal distribution as the sample size increases. d) All of the above are part of the Central Limit Theorem.

Q: 5 The sampling distribution of the mean is a) the population mean. b) the distribution of the population mean over many populations. c) the distribution of sample means over repeated samples. d) the mean of the distribution of the sample.

Q: 4 When we are using a two-tailed hypothesis test, the alternative hypothesis is of the form