Psy 2220 Exam 3 - HWK 5 + 6

Which of the following is an assumption of the independent-samples t test, but not an assumption of the one-sample t test?

Homogeneity of variance

In which of the following situations do we use a t distribution, instead of the z distribution, to conduct a hypothesis test comparing two means?

When we do not know the population standard deviation

Imagine that researchers appropriately conduct a paired-samples t test with 25 pairs of related scores. The mean difference between those 25 pairs of scores was 5.00. The standard deviation for the 25 difference scores was 7.50. What is the corresponding value for Cohen's d (rounded to three decimal places)? When computing your answer, please assume that the researchers are using a standard null hypothesis that predicts no differences.

0.667

Please consider the following information: Sample mean (M) = 50 Population mean (µ) = µM = 47 Sample standard deviation (s) = 4 Sample size (N) = 25 Based on this information, compute the effect size measure, Cohen's d. Please include at least two decimal places when reporting your answer.

0.75

Please consider the following information: Sample mean (M) = 65 Population mean (µ) = µM = 61 Sample standard deviation (s) = 8 Sample size (N) = 25 Based on this information, please compute the corresponding 95% confidence interval. Please type the lower boundary of the confidence interval as your answer. Please include at least three decimal places in your answer, if relevant.

61.6976

If the sample size (N) for a one-sample t test was 81, how many degrees of freedom would that t test have?

80

Imagine that a researcher conducts an experiment using a within-groups design. Specifically, the same participants provide related scores on a dependent variable at two different levels of an independent variable. (Please assume that a relevant population standard deviation is not known). Which of the following analyses would be appropriate for comparing means for both levels of the independent variable?

A paired-samples t test

Which of the following sampling distributions is used when conducting a paired-samples t test?

A sampling distribution of mean differences

Please consider the following information: Sample mean (M) = 52 Population mean (µ) = µM = 49 Sample standard deviation (s) = 15 Sample size (N) = 81 If a researcher used the information listed above and conducted a two-tailed hypothesis test with an alpha level (p level) of 0.05 (5%), should the researcher reject a typical null hypothesis of no differences between population means, based on the corresponding t test and the rules of hypothesis testing?

No. The researcher should fail to reject the null hypothesis.

Imagine that researchers appropriately conduct a paired-samples t test with 25 pairs of related scores. The mean difference between those 25 pairs of scores was 5.00. The standard deviation for the 25 difference scores was 7.50. Which of the following is the appropriate 95% confidence interval for these data (when reporting three decimal places)?

[1.904, 8.096]

Is the following statement true or false? If you appropriately compute a t statistic for 25 related pairs of scores (using JASP or a similar program), the t statistic will have the same absolute value as a correctly computed one-sample t statistic computed from the differences between those 25 pairs of related scores. Note: When answering, please assume that we have standard null hypotheses (indicating no differences) for two-tailed tests.

true

What would be the critical value for a one-tailed, one-sample t test with a sample size of 61 (N = 61) and an alpha level (p level) equal to 0.05 (5%)? Please provide at least three decimal places when reporting your answer. Please also provide only the absolute value of the answer (i.e., don't include a "+" symbol or "-" symbol).

1.671

Please consider the following data set. The initial row provides labels for two variables (i.e., X1 and X2). Each subsequent row represents a pair of related scores from the same person at two different points in time. X1: 2,6,7,3,8 X2: 4,7,6,5,9 Compute the appropriate t statistic to test the null hypothesis that there is no difference between means. When computing the t statistic, please retain a minimum of four decimal places for all intermediate steps (when relevant). For your final answer, please report the absolute value of the t statistic with a minimum of three decimal places.

1.826

Assume the blood pressures of 10 people were measured before and after sleeping for the night. What is the corresponding critical t-value for a one-tailed, paired-samples t test with an alpha level of 0.05 (5%). Please report your answer as an absolute value and include three decimal places.

1.833

Imagine that a researcher appropriately conducts a two-tailed, independent-samples t test with an alpha level of 0.05 (5%). The first group has degrees of freedom equal to 19. The second group has degrees of freedom equal to 21. What is the critical value (as a t statistic) that would cut off the upper 2.5% of the corresponding sampling distribution. Please provide three decimal places when reporting your answer.

2.021

What would be the critical value for a two-tailed, one-sample t test with 26 degrees of freedom (df = 26) and an alpha level (p level) equal to 0.05 (5%)? Please provide at least three decimal places when reporting your answer. Please also provide only the absolute value of the answer (i.e., don't include a "+" symbol or "-" symbol).

2.056

Please calculate the sample standard deviation for the following sample of five numbers: 2, 4, 6, 8, 10 Please provide at least two decimal places when reporting your answer.

3.16

Please consider the following information: Sample mean (M) = 50 Population mean (µ) = µM = 47 Sample standard deviation (s) = 4 Sample size (N) = 25 Based on this information, compute the t statistic for a one-sample t test. (You may need to compute some other values before computing the t statistic itself). When reporting your t statistic, please provide at least two decimal places.

3.75

Is the following statement true or false? As the sample size increases, the corresponding t distribution more closely approximates the z distribution.

True

Is the following statement true or false? We can not legitimately conduct an independent-samples t test if the sample sizes of our two groups are different.

false