Stats ch 9

If other factors are held constant, what is the effect of increasing the sample variance?

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

Which of the following is the correct null hypothesis for an independent-measures t test?

a. μ1 - μ2 = 0

Which of the following is not needed to compute a t statistic?

b. The value of the population variance or standard deviation

What is assumed by the homogeneity of variance assumption?

c. The two populations have equal variances.

If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?

d. If the samples are the same size and have the same mean and the same variance

Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large measure of effect size?

b. A large mean difference and small sample variances

The estimated standard error for the independent-measures t statistic provides a measure of how much difference should exist, on average, between two sample means when the null hypothesis is true.

True

Compared to a z-score, a hypothesis test with a t statistic requires more information from the sample. T or F

True

If other factors are held constant, as the sample variance increases, the estimated standard error also increases. T or F

True

The homogeneity of variance assumption states that the two population variances are equal.

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 or F

True

A hypothesis test with a sample of n= 25 participants produces a t statistic of t = +2.53. Assuming a one-tailed test with the critical region in the right-hand tail, what is the correct decision?

b. The researcher can reject the null hypothesis with either α = .05 or α = .01.

What value is estimated with a confidence interval using the t statistic?

b. The value for an unknown population mean

For an independent-measures study, the width of a confidence interval estimating μ1-μ2 depends on the size of the difference between M1 and M2. T or F

False

If two samples from the same population are the same size and have the same mean, then they will have the same t statistic. Tor F

False

In general, the larger the value of the sample variance, the greater the likelihood of rejecting the null hypothesis. T or F

False

Compared to a z-score, a hypothesis test with a t statistic requires less information from the population. T or F

True

Confidence intervals with the independent-measures t statistic are used to estimate how much difference there is between two population means. T or F

True

For a hypothesis test with the independent-measures t statistic, the null hypothesis states that the two population means are the same and the homogeneity assumption states that the two population variances are the same. T or F

True

If other factors are held constant, as the sample size increases, the estimated standard error decreases. T or F

True

If other factors are held constant, the bigger the s ample is, the greater the likelihood of rejecting the null hypothesis. T or F

True

If other factors are held constant, the larger the two sample sizes are, the greater the likelihood that the independent-measures t test will find a significant difference. T or F

True

If the two samples are the same size, the independent measures t statistic will have an even number for degrees of freedom. T or F

True

Which set of characteristics will produce the smallest value for the estimated standard error?

a. A large sample size and a small sample variance

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

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

Which of the following describes what a confidence interval does?

a. It uses a sample mean to estimate the corresponding population mean.

Assuming that there is a 5-point difference between the two sample means, which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic?

a. Large sample sizes and small sample variances

If other factors are held constant, how does sample variance influence the likelihood of rejecting the null hypothesis and measures of effect size such as r2 and Cohen's d?

a. Larger sample variance increases both the likelihood and measures of effect size.

An independent-measures research study uses two samples, each with n= 15 participants. If the data produce a t statistic of t = 2.760, which of the following is the correct decision for a two-tailed hypothesis test?

a. Reject the null hypothesis with α = .05 but fail to reject with α = .01

An independent-measures study comparing two treatment conditions produces a t statistic with df = 18. If the two samples are the same size, how many participants were in each of the samples?

b. 10

If an independent-measures design is being used to compare two treatment conditions, then how many different groups of participants would be needed and how many scores would there be for each participant?

b. 2 groups, 1 score each

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?

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

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

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

How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen's d?

b. Larger variance increases the standard error but decreases measures of effect size.

Why are t statistics more variable than z-scores?

b. The extra variability is caused by variations in the sample variance.

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

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

An independent-measures study uses n= 15 participants in each group to compare two treatment conditions. What is the df value for the t statistic for this study?

c. 28

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 for this study?

c. 38

If other factors are held constant, what is the effect of increasing the sample size?

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

The narrower the confidence interval, the more precise it is. With this in mind, which combination of factors will produce the most precise estimate of the difference between two population means?

c. Two samples of n = 50 and 80% confidence

A researcher predicts that scores in treatment A will be higher than scores in treatment B. If the mean for the 10 participants in treatment A is 4 points higher than the mean for the 10 participants in treatment B and the data produce t = 2.095, what decision should be made?

c. With α = .05, reject H0 for a one-tailed test but fail to reject for a two-tailed test

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?

d. The t statistic does not require any information about the population.

On average, what value is expected for the t statistic when the null hypothesis is true?

a. 0

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?

a. 19

Which of the following research situations would be most likely to use an independent-measures design?

c. Compare the mathematics skills for 9th-grade boys versus 9th-grade girls

An independent-measures research study uses two samples, each with n= 10 participants. If the data produce a t statistic of t = 2.095, which of the following is the correct decision for a two-tailed hypothesis test?

c. Fail to reject the null hypothesis with either α = .05 or α = .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?

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

A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 30, how many individuals were in the sample?

c. n = 31

If other factors are held constant, which of the following sets of data is most likely to satisfy the homogeneity of variance assumption?

d. The other 3 options are equally likely to satisfy the assumption.