stats exam #2

It is expected that a treatment will reduce scores on a variable. If α = 0.05, what is the critical t value for a one-tailed hypothesis test with n = 15?

-1.761

A vertical line drawn through a normal distribution at z = -0.60 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the body?

0.7257

A news poll showed that voters had no preference for either of three candidates. In this example, the probability of a vote for Candidate A equals

1/3

A sample of n = 16 scores has a standard error of σM = 4. What is the standard deviation of the normally distributed population from which the sample was obtained?

16

A sample of n = 4 scores has a variance of s2 = 64. What is the estimated standard error for the sample mean?

2

Two samples each have n = 4 scores. If the first sample has a variance of s2 = 10 and the second sample has a variance of s2 = 6, what is the estimated standard error for the sample mean difference?

2

A sample with a mean of M = 40 and a variance of s2 = 12 has an estimated standard error of 2 points. How many scores are in the sample?

3

An independent-measures study comparing two treatment conditions produces a tstatistic with df = 16. If the two samples are the same size, how many participants were in each of the samples?

9

Which of the following is required to locate proportions of area under the normal curve?

Compute a z-transformation AND find the probability of a z-score

In order for the shape of the sampling distribution of the mean to be approximately normal, which of the following conditions MUST be present? I. the sample size must be at least 30 II. the population distribution must be positively skewed III. the population distribution must be normal

Either I or III

Compared to a z-score, a hypothesis test with a t statistic requires less information from the sample.

FALSE

If two sample sizes are not equal, the pooled variance value will be closer to the individual sample variance that has a larger variance value.

FALSE

A research study compares the mean weight for a sample of n = 36 participants before they begin a dieting routine diet to their mean weight six weeks later. This is an example of an independent-measures design.

False

If a researcher rejects the null hypothesis when conducting a hypothesis test, it means that the sample data failed to provide sufficient evidence to conclude that the treatment had an effect.

False

It is possible for the probability of a Type I error (p-value) obtained from a t-test to be 0.

False

A sample of n = 81 scores is obtained from a population with µ = 80 and σ = 27. If the sample mean corresponds to a z-score of +2.33, what is the value of the sample mean?

M = 87

A sample of n = 81 scores is obtained from a population with µ = 80 and σ = 27. If the sample mean corresponds to a z-score of +2.33, what is the value of the sample mean? M = 83 M = 73 M = 77 M = 87

M = 87

Which of the following is NOT a characteristic of probability? Probability varies between 0 and 1. Probability can be stated as a fraction or decimal. Probability is most useful for describing fixed events rather than random events. Probability can never be negative.

Probability is most useful for describing fixed events rather than random events.

If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic?

The researcher must know the population median. The researcher must know the population variance or standard deviation. The researcher must know the population size. The researcher does not need to know any information about the population.

A sample of n = 25 scores produces a t statistic of t = +2.052. If the researcher is conducting a two-tailed hypothesis test, which of the following is the correct statistical decision?

The researcher should fail to reject the null hypothesis with either α = 0.05 or α = 0.01. This is impossible to determine based on the provided information.

A researcher selects a sample and administers a treatment for anxiety to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis (H1) say about the treatment?

The treatment multiplies each anxiety score by a constant. The treatment has an effect on anxiety.

Two samples from the same population both have n = 10 scores with M = 45. If the tstatistic is computed for each sample, then what is the relationship between the two tvalues?

The two t statistics will be identical. The sample with the smaller variance will produce the larger t statistic. There is no way to predict the relationship between the two t statistics.

A researcher conducts a research study to examine whether there is a difference between two treatments regarding anxiety. Which of the following is consistent conceptually with the null hypothesis?

There is a difference between the two treatments among the general population regarding anxiety. There is no difference between the two treatments among the general population regarding anxiety. The first treatment is less effective than the second treatment regarding anxiety. The second treatment is less effective than the first treatment regarding anxiety.

A Type II error occurs when a researcher concludes that a treatment has no effect when it actually does have an effect.

True

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called

a sample distribution

A sampling distribution of the sample mean represents _______

all measures that could be obtained in a given sample of a given size all scores that could be obtained in a population all sample means that could be obtained in samples of a given size from the same population

What does it mean to say that the sample mean is an unbiased estimator of the population mean?

all options are correct

A sampling distribution of the sample mean represents _______

all sample means that could be obtained in samples of a given size from the same population

A normal distribution is normally distributed with a mean of ____ and a variance of ____.

any value; any positive value

Regardless of the distribution of the population, the sampling distribution of sample means will be approximately normally distributed. What theory explains this?

central limit theorem

A researcher is interested in having as much ability as possible to identify a treatment effect if one really exists. Which of the following strategies should they employ?

change from a one-tailed test to a two-tailed test change the sample size from n = 25 to n = 100

Which statement below is consistent with making a Type I error?

concluding that a treatment has an effect when it really does concluding that a treatment has an effect when it really has no effect

What statement below is consistent with making a Type II error?

concluding that a treatment has an effect when it really does concluding that a treatment has no effect when it really has no effect concluding that a treatment has no effect when it really does

An independent-measures research study uses a total of 40 participants to compare two treatment conditions. What is the df value for the t statistic computed for the corresponding hypothesis test?

df = 18 df = 38

The mean of the sampling distribution of sample means is

equal to the population mean

A Type I error occurs when a treatment has an effect but the decision is to fail to reject the null hypothesis.

false

In a hypothesis test, if the sample data is determined to be in the critical region with α = 0.05, then all of the same sample data would still be in the critical region if α were changed to 0.01.

false

Larger sample sizes increase the likelihood that an independent-measures t test will find a statistically significant difference, as well as the computed value for Cohen's d.

false

A researcher conducts a hypothesis test using a sample from an unknown population. If df = 30 for the t statistic and M = 46 and s2 = 10, how many individuals were in the sample?

n = 29 n = 46 n = 31 n = 30

In order for the shape of the sampling distribution of the mean to be approximately normal, which of the following conditions MUST be present? I. the sample size must be at least 30 II. the population distribution must be positively skewed III. the population distribution must be normal III only I and II Both I and III I only Either I or III

not I only

What values are distributed along the x-axis for a sampling distribution of the sample mean?

sample means

If you made a histogram of a sampling distribution of the sample mean, what values are along the x-axis?

sample means and sample variances

Which of the following accurately describes the critical region?

sample means that are very unlikely to be obtained if the null hypothesis is true

A researcher is examining whether daily yoga reduces stress. The researcher assigns n = 7 individuals to engage in daily yoga for three months and finds an average stress score of M = 16 with SS = 123 after three months for individuals in this group. A second group of n = 6 individuals assigned to a control group for the three months had a stress score of M = 21 with SS = 141. Which of the following is most consistent with the results of conducting a one-tailed independent-measures t test with α = .05?

t = -1.61 and fail to reject the null hypothesis t = -1.83 and reject the null hypothesis t = -1.83 and fail to reject the null hypothesis

A researcher is examining whether daily yoga reduces stress. The researcher assigns n = 7 individuals to engage in daily yoga for three months and finds an average stress score of M = 16 with SS = 123. A second group of n = 6 individuals assigned to a control group for the three months had a stress score of M = 21 with SS = 141. Which of the following is most consistent with the results of conducting a one-tailed independent-measures t test with α = .05?

t = -1.83 and reject the null hypothesis

A researcher is examining whether daily yoga reduces stress. The researcher assigns n = 7 individuals to engage in daily yoga for three months and finds an average stress score of M = 16 with SS = 123. A second group of n = 6 individuals assigned to a control group for the three months had a stress score of M = 21 with SS = 141. Which of the following is most consistent with the results of conducting a one-tailed independent-measures ttest with α = .05?

t = -1.83 and reject the null hypothesis t = -1.83 and fail to reject the null hypothesis

What is necessary to determine the z-score, given a raw score in a particular set of scores?

the mean and standard deviation for the set

Which of the following is consistent with what r2 represents as a measure of effect size?

the portion of variability in a sample attributable to a treatment effect relative to the total variability in the sample

The normal distribution has all of the following characteristics, except that

the total area under the curve is greater than 1.0

A larger difference between two sample means increases the likelihood that an independent-measures ttest will find a statistically significant difference, as well as the computed value for Cohen's d.

true

Two samples are selected from a population, and a treatment is administered to the samples. If both samples have the same mean and the same variance, a researcher is more likely to reject the null hypothesis and find a significant treatment effect with a sample of n = 100 than with a sample of n = 4.

true

A sample of n = 64 scores is selected from a population with µ = 60 and σ = 10. If the sample mean is M = 57, what is the z-score for this sample mean?

z = -2.40

A researcher predicts that scores in treatment A will be higher than scores in treatment B. Which of the following is the correct null hypothesis for a one-tailed test evaluating this prediction?

µA ≥ µB µA ≤ µB

An instructor is interested in whether frequent feedback in their course to a small sample of students influences student performance. The instructor knows that final class scores are normally distributed with µ = 85 and σ = 6. Which is the alternative hypothesis for this research study?

µfrequent feedback = 85 µfrequent feedback ≥ 85

A sample of n = 49 scores with M = 43 is selected from a population with µ = 40 and with σ = 21. What is the standard error for the sample mean?

σM = 3