PY 211 Chapter 12 Study Questions

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.

B. compare one sample mean against a population mean.

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

D. all of the above

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.

a) H1 : µ ≠ 50.

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.

a) The sample mean of the college skiers was significantly different from the population mean.

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

a) compare two means.

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

a) narrower than

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.

a) the population is normally distributed.

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.

a) the population mean.

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.

a) the probability is .95 that the sample mean lies between 112.5 and 118.4.

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.

a) the probability is .95 that the true mean falls between 12.65 and 25.65.

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.

a) will approach normal for large sample sizes.

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.

a) will be close to the population mean.

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

b) 3

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.

b) N - 1.

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.

b) convey useful information to the reader about what you found.

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.

b) depends on the sample size.

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.

b) lose one degree of freedom because we estimate the population mean.

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.

b) smaller than the corresponding population variance.

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.

b) that the null hypothesis is true.

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

b) the standard deviation of the sample.

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

b) when it is clearer to the reader to talk about a percentage

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

b) when there is very little variability within groups

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.

c) the actual magnitude of the mean or difference between means.

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.

d) All of the above are part of the Central Limit Theorem.

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.

d) Confidence limits are the boundaries of confidence intervals.

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.

d) H0 : µ = 50.

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 (s^2). c) The sample size (N). d) The population variance (σ^2).

d) The population variance (σ^2).

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 α = .05. b) reject the null hypothesis at α = .01 c) retain the null hypothesis. d) We cannot solve this problem without knowing the sample size.

d) We cannot solve this problem without knowing the sample size.

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 (α).

d) a smaller significance level (α).

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

d) all of the above

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

d) both a and c

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

d) both b and c

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.

d) is associated with a probability statement about the location of a population mean.

In using a z test for testing a sample mean against a hypothesized population mean, the formula for z is a) z= x-µ/ σ b) z= x-µ/ σ c)z=∑(X-x)^2/ σ/√N d) none of the above

d) none of the above

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.

d) positive if the sample mean is larger than the hypothesized population mean.

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.

d) the sample mean would differ from the population mean by more than 1.96 standard errors only 5% of the time.

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.

d) this will happen a fixed percentage of the time.

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.

d) we have to call the result t if the sample variance is used.

Cohen's ˆd is an example of a) a measure of correlation. b) an r-family measure. c) a d-family measure. d) a correlational measure.

c) a d-family measure.

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.

c) a population estimate.

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.

c) approaches the normal distribution as its degrees of freedom increase.

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.

c) bimodal.

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.

c) t(34) = 3.60, p <.05.

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.

c) the difference between t and z is small for that many cases.

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.

c) the sampling distribution of the variance.

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

c) the standard deviation of the sampling distribution of the mean.