12.1 In one-sample tests of means we a) compare one sample mean with another. b)
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Question
12.1 In one-sample tests of means we
a) compare one sample mean with another.
b) compare one sample mean against a population mean
c) compare two sample means with each other.
d) compare a set of population means.
12.2 I want to test the hypothesis that children who experience daycare before the age of 3 do better in school than those who do not experience daycare. I have just described the
a) alternative hypothesis.
b) research hypothesis.
c) experimental hypothesis.
d) all of the above
12.3 When we are using a two-tailed hypothesis test, the null hypothesis is of the form
a) H1 : µ 50.
b) H1 : µ < 50.
c) H1 : µ > 50.
d) H0 : µ = 50.
12.4 When we are using a two-tailed hypothesis test, the alternative hypothesis is of the form
a) H1 : µ 50.
b) H1 : µ < 50.
c) H1 : µ > 50.
d) H0 : µ = 50.
12.5 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.
12.6 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.
12.7 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.
12.8 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.
12.9 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.
12.10 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
12.11 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
12.12 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.
12.13 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.
12.14 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 would
a) reject the null hypothesis at = .05.
b) reject the null hypothesis at = .01
c) retain the null hypothesis.
d) We cannot solve this problem without knowing the sample size.
12.15 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
12.16 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.
12.17 When you are using a one-sample t test, the degrees of freedom are
a) N.
b) N – 1.
c) N + 1.
d) N – 2.
12.18 In using a z test for testing a sample mean against a hypothesized population mean, the formula for z is
a) µ = Xz
b) µ = Xz
c) ( ) N XX z = 2
d) none of the above
12.19 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.
12.20 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.
12.21 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.
12.22 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.
12.23 The sampling distribution of the variance is
a) positively skewed.
b) negatively skewed.
c) normal.
d) rectangular.
12.24 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.
12.25 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.
12.26 If we have run a t test with 35 observations and have found a t 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.
12.27 Which of the following does NOT directly affect the magnitude of t?
a) The actual obtained difference (X - µ).
b) The magnitude of the sample variance (s2).
c) The sample size (N).
d) The population variance (2).
12.28 If we compute 95% confidence limits on the mean as 112.5 – 118.4, we can conclude that
a) 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.
12.29 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.
12.30 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
12.31 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.
12.32 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.
12.33 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.
12.34 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
12.35 All of the following increase the magnitude of the t statistic and/or the likelihood of rejecting H0 EXCEPT
a) 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 ().
12.36 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.
12.37 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.
12.38 A t 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
12.39 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
12.40 Cohen’s ˆ d is an example of
a) a measure of correlation.
b) an r-family measure.
c) a d-family measure.
d) a correlational measure.
12.41 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.
12.42 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
12.43 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
12.44 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.
12.45 If we compute a confidence interval as 12.65 µ 25.65, then we can conclude that
a) the probability is .95 that the true mean falls between 12.65 and 25.65.
b) 95% of the intervals we calculate will bracket µ.
c) the population mean is greater than 12.65.
d) the sample mean is a very precise estimate of the population mean.
12.46 The t 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.
12.47 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
12.48 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.
Explanation / Answer
12.1 In one-sample tests of means we
b) compare one sample mean against a population mean
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12.3 When we are using a two-tailed hypothesis test, the null hypothesis is of the form
d) H0 : µ = 50.
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12.4 When we are using a two-tailed hypothesis test, the alternative hypothesis is of the form
a) H1 : µ 50.
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12.6 Which of the following is NOT part of the Central Limit Theorem?
d) All of the above are part of the Central Limit Theorem.
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12.7 If the population from which we sample is normal, the sampling distribution of the mean
c) will be normal.
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