Stats Exam 2

Which combination of factors will produce the largest value for the standard error?

A small sample and a large standard deviation

A sample of n = 16 scores is selected from a population with μ = 100 and σ = 32. If the sample mean is M = 104, what is the z-score for this sample mean?

0.50

For a particular population, a sample of n = 4 scores has an expected value of 10. For the same population, a sample of n = 25 scores would have an expected value of _____.

10

If random samples, each with n = 4 scores, are selected from a normal population with μ = 80 and σ = 36, what is the standard error for the distribution of sample means?

18

A researcher conducts a hypothesis test using a sample of n = 20 from an unknown population. What is the df value for the t statistic?

19

A sample with a mean of M = 40 and a variance of s2 = 20 has an estimated standard error of 1 point. How many scores are in the sample?

20

For a particular population, a sample of n = 4 scores has a standard error of 6. For the same population, a sample of n = 16 scores would have a standard error of _____.

3

If random samples, each with n = 9 scores, are selected from a normal population with μ = 80 and σ = 18, how much difference, on average, should there be between a sample mean and the population mean?

6 points

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the expected value for the distribution of sample means?

80

For a population with μ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ____.

80;5

What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?

As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases.

With a = .05, how are the boundaries for the critical region of a two-tailed (non-directional) test determined?

Boundaries are drawn so there is 2.5% (.025) in each tail of the distribution

Which of the following will increase the power of a statistical test? -Change a from .05 to .01 -Change from a one-tailed test to a two-tailed test -Correct Change the sample size from n = 25 to n = 100 -None of the other options will increase power.

Change the sample size from n = 25 to n = 100

What is the consequence of a Type I error?

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

Even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean. What outcome is likely if this happens?

Fail to reject H0 and make a Type II error

Under what circumstances can a very small treatment effect still be significant?

If the sample size (n) is very large

When n is small (less than 30), how does the shape of the t distribution compare to the normal distribution?

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

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

A researcher conducts a hypothesis test to evaluate the effect of a treatment that is expected to increase scores. The hypothesis test produces a z-score of z = 2.27. If the researcher is using a one-tailed test, what is the correct statistical decision?

Reject the null hypothesis with a = .05 but not with a = .01

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 = .05 but not with a = .01.

Which of the following is a fundamental difference between the t statistic and a z-score?

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

With a = .05 and df = 8, the critical values for a two-tailed t test are t = ±2.306. Assuming all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t?

They would decrease (move closer to zero).

A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is M = 48 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?

d = 0.50

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

What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72?

s2 = 9 and sM = 1

With a = .01, the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ______.

t = ±2.947

Samples of n = 16 scores are selected from a population. If the distribution of sample means has an expected value of 40 and a standard error of 2, what are the mean and the standard deviation for the population?

μ = 40 and σ = 8