HSE230 Practice Test #3

If a hypothesis test is found to have power=.70, what is the probability that the test will result in a Type II error?

.30

A random sample of n=9 scores is obtained from a normal population with μ=40 and σ=18. What is the probability that the sample mean will be greater than M=43?

0.3085

A random sample of n=16 cores is obtained from a normal population with μ=40 and σ=8. What is the probability that the sample mean will be within 2 points of the population mean?

0.6826

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

16

A sample of n=4 scores is selected from a population with μ=40 and σ=8, and sample mean is M=43. What is the standard error for the sample mean?

4

A sample of n=4 scores is selected from a pop. with μ=40 and σ=8, and the sample mean is M=43. What is the expected value for the sample mean?

40

A sample of n=16 scores is selected from a population with μ=80 and σ=20. On average, how much error would be expected between the sample mean and the pop. mean?

5 points

If all the possible random samples with n=36 are selected from a normal population with μ=80 and σ=18, and the mean is calculated for each sample, what is the average of all sample means?

80

If a treatment has a very small effect, what is a likely outcome for a hypothesis test evaluating the treatment?

A Type II error

A researcher administers a treatment to a sample of participants selected from a population with μ=80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis?

A sample mean much different than 80 for a large sample.

What is the effect of decreasing the alpha level (for example, from a=0.05 to a=0.01)

All of these choices are results of the critical region; decreases size of critical region, decreases probability of a Type I error, decreases probability that the sample will fall into the critical region

Which of the following accurately describes the effect of increasing the sample size?

Decreases the standard error and has no effect on the risk of a Type I error.

Which of the following is an accurate definition of a Type II error?

Failing to reject a false null hypothesis

A researcher administers a treatment to a sample of n=16 selected from a pop. with μ=40 and σ=8. If the sample mean after treatment is M=42, then Cohen's d=1.00

False

A sample of n=25 scores is selected from a pop. with μ=70 and σ=20. It is very unlikely that the sample mean will be greater than 72.

False

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 standard error for the sample mean is 20.

False

A sample of n=4 scores is selected from a normal pop. with μ=30 and σ=8. The probability of obtaining a sample mean greater than 34 is equal to the probability of obtaining a z-score greater than z=2.00.

False

If a hypothesis test rejects the null hypothesis using an alpha level of a=0.05 then the research report would include the statement, "p>.05"

False

If other factors are held constant, lowering the alpha level will increase the power of a hypothesis test.

False

In a hypothesis test, the likelihood of rejecting the null hypothesis is independent of the sample size.

False

The mean for a sample of n=9 scores has a standard error of 2 points. This sample was selected from a pop. with a standard deviation of σ=18.

False

The null hypothesis states that the sample mean (after treatment) is equal to the original pop. mean (before treatment)

False

The power of a hypothesis test is the probability that the sample mean will be in critical region even if the treatment has no effect

False

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

False

A Type II error occurs when a researcher concludes that a treatment has an effect but, in fact, the treatment has no effect.

False.

Under what circumstances will the distribution of sample means be normal?

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

Which of the following correctly describes the effect of increasing the alpha level (for example, from .01 to .05)?

Increase the likelihood of rejecting H0 and increase the risk of a Type I error.

What happens to the expected value of M as a sample size increases?

It stays constant.

A sample of n=4 scores is obtained from a population with μ=70 and σ=8. If the sample mean corresponds to a z-score of 2.00, what is the value of the sample mean?

M=78

A treatment is administered to a sample of n=9 individuals selected from a pop. with a mean of μ=80 and a standard deviation of σ=12. After treatment, the effect size is measure by computing Cohen's d, and a value of d=0.50 is obtained. Based on this information, what is the mean for the treated sample?

M=86

Even if a treatment has no effect, it is still possible to obtain an extreme sample mean that is very different from the population mean. What outcome is likely if this happens?

Reject H0 and make a Type I error.

Which of the following is an accurate definition of a Type I error?

Rejecting a true null hypothesis

A random sample of n=60 scores is selected from a population. Which of the following distributions definitely will be normal?

The distribution of sample means will form a normal distribution.

What is measured by the numerator of the z-score test statistic?

The actual distance between M and μ

A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z=2.37. Assuming that the researcher is using a two-tailed test, what decision should be made?

The researcher should reject the null hypothesis with a=0.05 but not with a=0.01

A random sample of n=6 scores is selected from a population. Which of the following distributions definitely will be normal?

The sample, the population, and the distribution of sample means definitely will not be normal

A sample is selected from a population with σ=10 and μ=30. If the sample mean of M=34 corresponds to z=2.00, then the sample size is n=25.

True

A sample of n=9 scores is selected from a normal population with a mean of μ=80 and a standard deviation of σ=12. The probability that the sample mean will be greater than M=86 is equal to the probability of obtaining a z-score greater than z=1.50

True

Although the size of the sample can influence the outcome of a hypothesis test, it has little or no influence on measures of effect size.

True

As the population standard deviation increases, the standard error will also increase

True

If samples are selected from a normal population, the distribution of sample means will also be normal.

True

On average, a sample of n=16 scores will provide a better estimate of the population mean than you would get with a sample of n=9 scores from the same population.

True

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

True

When is there a risk of a Type I error?

Whenever H0 is rejected

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?

You have made a Type I error.

You complete a hypothesis test using a = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?

You have made a correct decision

A sample from a population with μ=40 and σ=8 has a mean of M=36. If the sample mean corresponds to z=-1.00, then how many scores are in a sample?

n=4

A sample of n=4 scores is selected from a normal population with a mean of μ=50 and a standard deviation of σ=20. What is the probability of obtaining a sample mean greater than M=48?

p=0.5793

For a normal population with a mean of μ=80 and a standard deviation of σ=10, what is the probability of obtaining a sample mean greater than M=75 for a sample of n=25 scores?

p=0.9938

A sample of n=9 scores is obtained from a pop. with μ=70 and σ=18. If the sample mean is M=76, what is the z-score for the sample?

z=1.00