test 2

A researcher finds that 20 out of 120 students failed an exam. In this case, the probability of failing this exam was _____. .17 .14 .20 None of the above

.17

A researcher has participants choose between three advertisements. She finds that 54 participants prefer advertisement A, 86 participants prefer advertisement B, and 60 participants prefer advertisement C. The probability or proportion of participants preferring advertisement B is _____. .86 .43 86 .60

.43

On average, what value is expected for the t-statistic when the null hypothesis is true? 1 +1.96 0 -1.96

0

What proportion of a normal distribution is located between the mean and z = -0.40? 0.3108 0.6554 0.3446 0.1554

0.1554

What is the probability of randomly selecting a z-score greater than z = +0.75 from a normal distribution? 0.4532 0.7734 0.2266 0.2734

0.2266

What is the probability of randomly selected a z-score less than z = +1.25 from a normal distribution? 0.2112 0.1056 0.8944 0.3944

0.8944

A jar contains 10 red marbles and 30 blue marbles. A random sample without replacement of n = 3 marbles is selected from the jar. If the first two marbles are both blue, what is the probability that the third marble will be red? 8/38 10/37 10/40 10/38

10/38

A jar contains 15 red marbles and 30 blue marbles. What is the probability of randomly selecting a red marble from the jar? 1/15 1/45 15/30 15/45

15/45

Which set of characteristics will produce the smallest value for the estimated standard error? A small sample size and a large sample variance. A large sample size and a large sample variance. A large sample size and a small sample variance. A small sample size and a small sample variance.

A large sample size and a small sample variance.

If other factors are held constant, how does sample size influence the likelihood of rejecting the null hypothesis and measures of effect size such as r² and Cohen's d? A larger sample decreases the likelihood but has little influence on measures of effect size. A larger sample increases both the likelihood and measures of effect size. A larger sample decreases both the likelihood and measures of effect size. A larger sample increases the likelihood but has little influence on measures of effect size.

A larger sample increases the likelihood but has little influence on measures of effect size.

Under what circumstances is the distribution of sample means normal? Only if the population distribution is normal. It is always normal. If the population is normal or if the sample size is greater than 30. If the sample size is greater than 30.

If the population is normal or if the sample size is greater than 30.

Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means? The fact that sample means vary minimally from the population mean The central limit theorem The fact that increasing sample size will increase standard error The skewed distribution rule

The central limit theorem

What term is used to identify the mean of the distribution of sample means? The standard error of M The expected value of M The sample mean The central limit theorem

The expected value of M

To compute a one-sample t-test a researcher has to know several values. Which of the following is NOT a value that the researcher must know to compute this test? The sample variance The estimated standard error The population variance The sample size

The population variance

Which of the following is an important aspect of probability? Combined probabilities of events that occur at the same time is equal to 1.0. All possible outcomes have the exact same probability of occurring. The sum of probabilities of all possible outcomes of an event equals 1.0. Each outcome has a 50% chance of occurring.

The sum of probabilities of all possible outcomes of an event equals 1.0.

Which of the following is a fundamental difference between the t-statistic and a z-score? The t statistic is used for large samples only. The t statistic uses the sample variance in place of the population variance. The t statistic uses the sample mean in place of the population mean. The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n.

The t statistic uses the sample variance in place of the population variance.

Probability values are always _____. positive numbers greater than or equal to 0 less than or equal to 1 All of the above

all of the above

he distribution of samples means _____. is used to find the median. is based on an infinite number of z-scores. is also known as a normal curve. helps researchers evaluate sample means.

helps researchers evaluate sample means

Conceptually, probability is most similar to the concept of _____. division likelihood proof certainty

likelihood

The _____ hypothesis states that there is no difference or relationship among groups and the _____ hypothesis states that there is a difference or relationship among groups. null; alternative statistical; null alternative; null null; statistical

null; alternative

If you were to _____ the null hypothesis, you would say the result is statistically _____. fail to reject; significant reject; nonsignificant fail to reject; proven reject; significant

reject; significant

The process of hypothesis testing starts with the assumption that the research hypothesis is true. the alternative hypothesis is true unless the data proves otherwise. the null hypothesis is yet to be defined. the null hypothesis is true.

the null hypothesis is true.

Mathematically, probability may be defined as the number of ways an outcome may occur. the total number of possible outcomes minus the number of ways a particular outcome may occur. the likelihood of rejecting a null hypothesis. the number of ways an outcome may occur divided by the total number of possible outcomes.

the number of ways an outcome may occur divided by the total number of possible outcomes.

Looking at the degrees of freedom value tells you something about _____. the null hypothesis the directionality of the hypothesis test the size of the sample the alpha level

the size of the sample

What term is used to identify the standard deviation of the distribution of sample means? The central limit theorem The expected value of M The standard error of M The sample mean

the standard error of M

The critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true. (t/f)

true

The null hypothesis is stated in terms of the population, even though the data come from a sample.

true

The t distribution for df = 4 is flatter and more spread out than the t distribution for df = 20. (t/f)

true

When the population variance or standard deviation is not known, you must use a t statistic instead of a z-score for a hypothesis test. (t/f)

true

When the z-score value in a normal distribution is negative, the majority of the area is on the right-hand side of the distribution. (t/f)

true

A statistically significant treatment effect does not necessarily indicate a large treatment effect. (t/f)

true

According to the central limit theorem, the standard error for a sample mean becomes smaller as the sample size increases.(T/F)

true

All probabilities can be expressed as decimal values ranging from 0 to 1.00. (t/f)

true

Although hypothesis tests are influenced by sample size, it has little or no influence on measures of effect size, such as r² and Cohen's d. (t/f)

true

For a normal distribution, the proportion in the tail beyond z = +1.50 is p = 0.0668. (t/f)

true

For any normal distribution, exactly 97.50% of the z-score values are less than z = +1.96. (t/f)

true

For any normal distribution, the z-score boundary that separates the lowest 2.5% of the scores from the rest is z = -1.96. (t/f)

true

If other factors are held constant, as the sample size increases, the estimated standard error decreases. (t/f)

true

If other factors are held constant, as the sample variance increases, the estimated standard error also increases. (t/f)

true

If other factors are held constant, the larger the sample is, the greater the likelihood of rejecting the null hypothesis. (t/f)

true

If samples are selected from a normal population, the distribution of sample means will also be normal.(T/F)

true

In a research report, the notation p < .05 indicates that the probability of a Type I error is less than .05 (or less than 5%).

true

In general, the null hypothesis states that the treatment has no effect on the population parameter being studied. (t/f)

true

One of the simplest and most direct methods for measuring effect size is Cohen's d. (t/f)

true

What happens to the standard error of M as the sample size increases? The standard error does not change in a predictable manner when the sample size increases. It decreases. It stays constant. It also increases.

it decreases

What happens to the expected value of M as the sample size increases? It stays constant. The expected value does not change in a predictable manner when the sample size increases. It also increases. It decreases.

it stays constant

The _____ of the distribution of sample means is equal to _____. mean; 0 variability; 0 variability; 1 mean; μ

mean; μ

By definition, the probability of an outcome or event is the fraction of times an outcome is likely to occur. particularly useful for predicting the likelihood of random events. the proportion of times an outcome is likely to occur. All of the above

All of the above

Which of the following are requirements of a random sample? Every individual has an equal chance of being selected There must be sampling with replacement The probabilities cannot change during a series of selections All of the above

All of the above

Which of the following accurately describes a hypothesis test? An inferential technique that uses the data from a sample to draw inferences about a population. A descriptive technique that allows researchers to describe a population. An inferential technique that uses information about a population to make predictions about a sample. A descriptive technique that allows researchers to describe a sample.

An inferential technique that uses the data from a sample to draw inferences about a population.

In which of the following steps of analyzing data is probability most important? Calculating inferential statistics. Calculating measures of central tendency such as the mean or median. Calculating the number of scores in your sample of collected data. Examining your data by creating tables and figures.

Calculating inferential statistics.

What is the consequence of 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. Concluding that a treatment has no effect when it really has no effect. Concluding that a treatment has no effect when it really does.

Concluding that a treatment has an effect when it really has no effect.

What is the consequence of a Type II error? Concluding that a treatment has no effect when it really does. Concluding that a treatment has no effect when it really has no effect. Concluding that a treatment has an effect when it really does. Concluding that a treatment has an effect when it really has no effect.

Concluding that a treatment has no effect when it really does.

Which of the following is an accurate definition of a Type II error? Failing to reject a false null hypothesis Failing to reject a true null hypothesis Rejecting a false null hypothesis Rejecting a true null hypothesis

Failing to reject a false null hypothesis

Under what circumstances can a very small treatment effect be statistically significant? If the sample size is big and the sample variance is small. If the sample size and the sample variance are both large. If the sample size is small and the sample variance is large. If the sample size and the sample variance are both small.

If the sample size is big and the sample variance is small.

What does it mean to say that the sample mean is an unbiased estimator of the population mean? If we select a sample mean at random, then on average we can expect the sample mean to equal the population mean. The distribution of sample means is typically negatively skewed. The sample means will vary minimally from the population mean. All of the above

If we select a sample mean at random, then on average we can expect the sample mean to equal the population mean.

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution? There is no consistent relationship between the t distribution and the normal distribution. It is taller and narrower than the normal distribution. It is flatter and more spread out than the normal distribution. It is almost perfectly normal.

It is flatter and more spread out than the normal distribution.

If other factors are held constant, what is the effect of increasing the sample size? It will increase the estimated standard error and increase the likelihood of rejecting the null hypothesis. It will increase the estimated standard error and decrease the likelihood of rejecting the null hypothesis. It will decrease the estimated standard error and decrease the likelihood of rejecting the null hypothesis. It will decrease the estimated standard error and increase the likelihood of rejecting the null hypothesis.

It will decrease the estimated standard error and increase the likelihood of rejecting the null hypothesis.

If other factors are held constant, what is the effect of increasing the sample variance? It will increase the estimated standard error and decrease the likelihood of rejecting the null hypothesis. It will decrease the estimated standard error and decrease the likelihood of rejecting the null hypothesis. It will decrease the estimated standard error and increase the likelihood of rejecting the null hypothesis. It will increase the estimated standard error and increase the likelihood of rejecting the null hypothesis.

It will increase the estimated standard error and decrease the likelihood of rejecting the null hypothesis.

Which of the following accurately describes the critical region? Outcomes with a high probability if the null hypothesis is true. Outcomes with a high probability whether or not the null hypothesis is true. Outcomes with a very low probability whether or not the null hypothesis is true. Outcomes with a very low probability if the null hypothesis is true.

Outcomes with a very low probability if the null hypothesis is true.

Two researchers select a sample from a population with a mean of 12.4 and a standard deviation of 9. Researcher A selects a sample of 30 participants and Researcher B selects a sample of 40 participants. Which sample is associated with a smaller standard error? Researcher A because the sample size was smaller. Researcher A because the sample size was larger. Researcher B because the sample size was larger. Researcher B because the sample size was smaller.

Researcher B because the sample size was larger.

If the standard deviation for a population increases, the standard error for sample means from that population will also increase.(T/F)

True

The distribution of sample means is the collection of sample means for all of the possible random samples of a particular size (n) that can be obtained from a population.(T/F)

True

The law of large numbers states that the larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.(T/F)

True

The sampling error is the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.(T/F)

True

Two samples will probably have different means even if they are both the same size and they both are selected from the same population. (T/F)

True

Which of the following is NOT one of the steps of hypothesis testing? Compute the test statistic Evaluate the plan State the hypotheses Set the criteria for a decision

evaluate the plan

When is there a risk of a Type II error? The risk of a Type II error is independent of the decision from the hypothesis test Whenever the alternative hypothesis is rejected. Whenever the null hypothesis is rejected. Whenever the decision is to fail to reject the null hypothesis.

Whenever the decision is to fail to reject the null hypothesis

When is there a risk of a Type I error? Whenever the alternative hypothesis is rejected. Whenever the decision is to fail to reject the null hypothesis. Whenever the null hypothesis is rejected. The risk of a Type I error is independent of the decision from the hypothesis test.

Whenever the null hypothesis is rejected.

The null and alternative hypotheses _____. state the critical values of a statistic needed to reject the null hypothesis. contain values of a sample statistic such as the sample mean (M) are two types of research hypotheses are mutually exclusive

are mutually exclusive

What is the sufficient sample size to use for the central limit theorem? at least 40 at least 25 at least 30 at least 26

at least 30

As sample size increases, the standard error of the mean can increase or decrease. decreases. increases. does not change.

decreases

The distribution of sample means helps determine whether a set of data is skewed or asymmetric. determine the probability of obtaining a particular value of a sample mean. determine the probability of obtaining a particular value of the population mean. describe the shape of a data sample.

determine the probability of obtaining a particular value of a sample mean.

The statement "μ > 8" is an example of a directional null hypothesis. non-directional alternative hypothesis. non-directional null hypothesis. directional alternative hypothesis.

directional alternatives hypothesis

The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = -1.85, then what is the correct statistical decision? Reject null hypothesis Fail to reject alternative hypothesis Reject alternative hypothesis Fail to reject null hypothesis

fail to reject null hypothesis

A jar contains 10 red marbles and 20 blue marbles. If you take a random sample with replacement of n = 2 marbles from this jar and the first marble is blue, then the probability that the second marble is blue is p = 19/29. (t/f)

false

A vertical line drawn through a normal distribution at z = -0.75 will separate the distribution into two sections. The proportion in the smaller section is 0.2734. (t/f)

false

As the sample size increases, the standard error also increases.(T/F)

false

As the sample size is increased, the distribution of t statistics becomes flatter and more spread out. (t/f)

false

For a normal distribution, proportions in the right-hand tail are positive values and the proportions in the left-hand tail are negative values. (t/f)

false

For a normal distribution, the proportion located between z = -1.00 and z = +1.00 is p = 34.13%. (t/f)

false

For any normal distribution, the proportion located between the mean and z = +1.40 is p = 0.9192. (t/f)

false

If two samples each have the same mean, the same number of scores, and are selected from the same population, then they will also have identical t statistics. (t/f)

false

In a hypothesis test, a large value for the sample variance increases the likelihood that you will find a significant treatment effect. (t/f)

false

In general, the larger the value of the sample variance, the greater the likelihood of rejecting the null hypothesis. (t/f)

false

The alpha level determines the risk of a Type II error.

false

You can reduce the risk of a Type I error by using a larger sample size.

false

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 35, how many individuals were in the sample? n = 36 n = 33 n = 34 n = 35

n=36

The statement "μ ≠ 8" is an example of a directional alternative hypothesis. non-directional alternative hypothesis. directional null hypothesis. non-directional null hypothesis.

non-directional alternative hypothesis.

The central limit theorem states that when an infinite number of random samples are drawn from a population, the sample means are approximately normally distributed when a mean equal to the _____ and a standard deviation equal to the _____ of the mean. population mean; standard error population mean; standard deviation sample mean; standard deviation sample mean; standard error

population mean; standard error

Which of the following is an accurate definition of a Type I error? Rejecting a true null hypothesis Failing to reject a false null hypothesis Rejecting a false null hypothesis Failing to reject a true null hypothesis

rejecting a true null hypothesis

Probability is an important concept for researchers primarily because most research involves flipping coins and pulling aces out of a deck of cards. researchers test hypotheses about samples by collecting data from populations. researchers collect data from samples rather than populations. it helps researchers prove their hypotheses.

researchers collect data from samples rather than populations.

With α = .05, what is the critical t value for a one-tailed test with n = 15? t = 1.761 t = 2.145 t = 1.753 t = 2.131

t = 1.761

With α = .01, the two-tailed critical region for a t-test using a sample of n = 16 participants would have boundaries of _____. t = ±2.583 t = ±2.602 t = ±2.947 t = ±2.921

t = ±2.947

The decision to use a directional versus non-directional hypothesis test most directly affects _____. the alpha level the critical value(s) the degrees of freedom the sample size

the critical value(s)

A researcher draws a random sample of 25 people from a population and calculates the mean of their IQs. If she were to repeat this process of drawing samples and calculating means an infinite number of times, the sample means could be used to create _____. z-scores critical values the distribution of sample means research hypotheses

the distribution of the sample means

A directional hypothesis test is also referred to as a one-tailed test. (t/f)

true

A mathematical proposition known as the central limit theorem provides a precise description of the distribution that would be obtained if you selected every possible sample, calculated every sample mean, and constructed the distribution of the sample mean.(T/F)

true

A measure of effect size is intended to provide a measurement of the absolute magnitude of a treatment effect.

true

A sample of n = 25 scores is selected from a population with a mean of µ = 80 and a standard deviation of σ = 20. The expected value for the sample mean is 80.(T/F)

true