Quiz 5 (chapters 9-10)

A hypothesis test produces a t statistic of t = 2.20. If the researcher is using a two-tailed t test with alpha = 0.05, how large does the sample have to be in order to reject the null hypothesis? at least n = 12 at least n = 13 at least n = 14 at least n = 11

n = 13

With alpha = 0.01, the two-tailed critical region for a t test using a sample of n = 16 subjects would have boundaries of ____. t = +/- 2.921 t = +/- 2.602 t = +/- 2.583 t = +/- 2.947

t = +/- 2.947

A sample of n=4 scores has SS=48. What is the estimated standard error of the mean?

2.0 (s = sqrt(48/3) = sqrt(16) = 4; sM = s/sqrt(n) = 4/2 = 2)

A sample with a mean of M=40 and a variance of s2 = 20 has an estimated standard error of 2 points. How many scores are in the sample?

5 (If s2 = 20, and sM = sqrt(s2/n), then 2 = sqrt(20/n), so 4 = 20/n, so 4n = 20, so n=5)

A sample of n = 4 scores has SS = 60. What is the variance for this sample?

20 (sample variance = SS/df = SS/(4-1) = 60/3 = 20. )

If other factors are held constant, which set of sample characteristics is most likely to lead to rejection of a null hypothesis stating that mu = 80? M = 90 and large sample variance M = 90 and small sample variance M = 85 and small sample variance M = 85 and large sample variance

M = 90 and small sample variance

Which of the following samples will have the smallest value for the estimated standard error? n = 100 with s2 = 400 n = 25 with s2 = 100 n = 25 with s2 = 400 n = 100 with s2 = 100

n = 100 with s2 = 100

When n is small (less than "hundreds"), 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 can be either flatter/broader or taller/narrower than the normal distribution depending on the degrees of freedom. It is flatter and more spread out than the normal distribution. It is taller and narrower than the normal distribution

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

Which combination of factors is most likely to produce a significant value for an independent-measures t statistic? large samples and small sample variances large samples and large sample variances small samples and large sample variances small samples and small sample variances

large samples and small sample variances

A sample of n = 4 scores is selected from a population with an unknown mean. The sample has a mean of M = 40 and a variance of s2 = 16. Which of the following is the correct 90% confidence interval for mu? mu = 40 +/- 3.276 mu = 40 +/- 9.412 mu = 40 +/- 4.706 mu = 40 +/- 6.552

mu = 40 +/- 4.706 (that is, mu = 40 +/- (2.353*2).

A sample is selected from a population with mu = 46 and a treatment is administered to the sample. The null hypothesis is rejected during hypothesis testing. After treatment, the sample mean is M=48 with a sample variance of s2 = 16. Based on this information, the size of the treatment, as measured by the estimated Cohen's d, is ______. NOTE: Assume that the effect size is always reported as a positive number.

0.5 (the estimated Cohen's d is 0.50. Specifically, d = (M-mu)/s = (46-48)/sqrt(16) = -2/4 = -0.50, reported as a positive number is 0.50)

A sample of n = 25 scores has a mean of M=40 and a variance of s2 = 100. What is the estimated standard error of the mean?

2 (Specifically, s = sqrt(100) = 10, and sM = s/sqrt(n) = 10/sqrt(25) = 10/5 = 2.)

Two samples, each with n=8, produce an independent-measures t statistic of t = -2.12 in a two-tailed hypothesis test. Which of the following decisions is justified? Fail to reject the null hypothesis with either alpha=0.05 or alpha=0.01. Reject the null hypothesis with either alpha=0.05 or alpha=0.01. Fail to reject the null hypothesis with alpha = 0.05 but reject the null hypothesis with alpha = 0.01. Reject the null hypothesis with alpha=0.05 but fail to reject with alpha=0.01.

Fail to reject the null hypothesis with either alpha=0.05 or alpha=0.01. (This is because, for 14 degrees of freedom, tcrit for alpha = 0.05 equals 2.14. (Positive or negative makes no difference, as that is arbitrary depending on which mean you subtract from the other mean).)

A sample has a mean of M = 39.5 and a standard deviation of s = 4.3, and produces a t statistic of t = 2.14. For a two-tailed hypothesis test with alpha = 0.05, what is the correct statistical decision for this sample? The researcher must fail to reject the null hypothesis with either alpha = 0.05 or alpha = 0.01. It is impossible to make a decision about H0 without more information. The researcher can reject the null hypothesis with either alpha = 0.05 or alpha = 0.01. The researcher can reject the null hypothesis with alpha = 0.05 but not with alpha = 0.01.

It is impossible to make a decision about H0 without more information. (namely, df)

If other factors are held constant, what is the effect of increasing the sample variance? It will increase the estimated standard error and increase the likelihood of rejecting H0. It will increase the estimated standard error and decrease the likelihood of rejecting H0. It will decrease the estimated standard error and increase the likelihood of rejecting H0. It will decrease the estimated standard error and decrease the likelihood of rejecting H0.

It will increase the estimated standard error and decrease the likelihood of rejecting H0.

If other factors are held constant, which set of sample characteristics is most likely to lead to the rejection of a null hypothesis stating that mu = 80? M = 90 for a sample of n = 100 M = 85 for a sample of n = 25 M = 90 for a sample of n = 25 M = 85 for a sample of n = 100

M = 90 for a sample of n = 100

An independent-measures research study uses two samples, each with n=12 participants. If the data produce a t statistic of t=2.08, then which of the following is the correct decision for a two-tailed hypothesis test? Reject the null hypothesis with either alpha=0.05 or alpha=0.01. Fail to reject the null hypothesis with either alpha=0.05 or alpha=0.01. Cannot answer without additional information. Reject the null hypothesis with alpha=0.05 but fail to reject with alpha=0.01.

Reject the null hypothesis with alpha=0.05 but fail to reject with alpha=0.01. (This is because, for 22 degrees of freedom, t=2.08 exceeds 2.07 (tcrit for alpha = 0.05) but does not exceed 2.82 (tcrit for alpha = 0.01).

A sample of n = 25 scores produces a t statistic of t = -2.062. If the researcher is using a two-tailed test, then which of the following is the correct statistical decision? The researcher must fail to reject the null hypothesis with either alpha = 0.05 or alpha = 0.01. It is impossible to make a decision about H0 without more information. The researcher can reject the null hypothesis with alpha = 0.05 but not with alpha = 0.01. The researcher can reject the null hypothesis with either alpha = 0.05 or alpha = 0.01.

The researcher must fail to reject the null hypothesis with either alpha = 0.05 or alpha = 0.01.

Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then what is the relationship between the two t values? There is no way to predict the relationship between the two t statistics The sample with the larger variance will produce the larger t statistic The sample with the smaller variance will produce the larger t statistic The two t statistics will be identical

The sample with the smaller variance will produce the larger t statistic

For an independent-measures research study, what is measured by Cohen's d or r2? The risk of a Type II error. The risk of a Type I error. The size of the difference between the two treatments. Whether the difference between the two treatments is likely to have occurred by chance.

The size of the difference between the two treatments.

In an independent-measures hypothesis test, what must be true if t=0? The two sample variances must be equal. None of the other three choices is correct. The two sample means must be equal. The two population means must be equal.

The two sample means must be equal.

With alpha = 0.05 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? There is not enough information to answer this question They would increase (move farther from zero) They would stay the same They would decrease (move closer to zero)

They would decrease (move closer to zero)

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

When the sample size is large and the sample variance is small

The results of a hypothesis test are reported as follows: t(15) = 2.70, p < 0.05. Based on this report, how many individuals were in the sample? cannot be determined from the information provided. 16 15 14

n = 16

If a sample of n = 16 scores is being used to make an 80% confidence interval estimate of the population mean mu, what value(s) of t should be used? t = +/- 2.131 t = 0 t = +/- 1.341 t = +/- 1.753

t = +/- 1.341