Question 1

Which of the following statements is true about t distributions?

Accepted Answer

As the sample size increases, the t distribution approaches the shape of a normal distribution. Option A is incorrect as there are infinitely many t distributions, not just 10. Option B is incorrect as there is only one appropriate t distribution for a given sample size. Option D is incorrect as t distributions are usually unimodal.

Question 2

If a sample includes 27 people,the degrees of freedom used in the formula to estimate the population variance would be

Accepted Answer

The degrees of freedom used in the formula to estimate the population variance is (n-1), where n is the sample size. Therefore, for a sample size of 27, the degrees of freedom would be (27-1) = 26. Thus, the correct choice is A) 26.

Question 3

A t test for dependent means would be used to compare

Accepted Answer

A t test for dependent means, also known as a paired samples t-test, is used to compare two means from the same group under different conditions or at different times. In this case, the level of reading comprehension of students is being compared at the beginning and at the end of a speed-reading class.

Question 4

A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4.
-If the psychologist figures S = .85,the effect size (d)is

Accepted Answer

The effect size (d) is calculated by taking the difference between the mean score of the sample and the mean score of the population, then dividing by the standard deviation of the sample. Thus, (5 - 4.4) / .85 = 0.71.

Question 5

The main difference between a Z score and a t score is that

Accepted Answer

The main difference between a Z score and a t score is that t scores are used when the population variance is unknown. Z scores are used when the population variance is known. T scores also take into account the sample size, which makes them more suitable for smaller sample sizes.

Question 6

The process of estimating the population variance from the scores in the sample involves

Accepted Answer

To estimate the population variance from the sample, we need to divide the sum of squared deviations by N - 1 instead of N. This is known as the formula for the sample variance, which corrects for the fact that we have one less degree of freedom (i.e., one less independent observation) in the sample compared to the population. This adjustment allows us to obtain an unbiased estimate of the population variance that takes into account the variability of the sample. Thus, the correct choice is C. The other choices are incorrect because there is no special table for estimating the variance, we do not need to interpret the results with more caution than usual, and we do not need to multiply the sample variance by the degrees of freedom.

Question 7

A t test for a single sample would be used to compare

Accepted Answer

A t-test for a single sample is used to compare the mean of a single sample to a known value or theoretical expectation (in this case, the hours that "C" average students spend on Facebook each week compared to an expected value, such as the average for students in general). Choices A, B, and C involve comparing two different groups or the same group at two different times, which would require different types of t-tests or statistical analyses.

Question 8

When conducting a t test for dependent means,μM

Accepted Answer

When conducting a t test for dependent means, μM is the population mean of the differences between the two dependent means. Since the differences are calculated by subtracting one mean from the other, the average difference is zero, which means that μM is always equal to 0.

Question 9

In the formula for estimating the population variance from the sample,the sum of squared deviations is divided by

Accepted Answer

When estimating the population variance from the sample, we use Bessel's correction and divide the sum of squared deviations by the number of participants in the sample minus one. This corrects for the tendency of the sample variance to underestimate the population variance. Therefore, the correct choice is B.

Question 10

If a sample includes three individuals with scores of 2,3,and 4,the estimated population variance is

Accepted Answer

The answer of If a sample includes three individuals with...

Question 11

The difference between a t test for a single sample and a Z test for a single sample is the way

Accepted Answer

The primary difference between a t-test and a Z-test for a single sample lies in how the variance of the known population is determined. A t-test is used when the population variance is unknown and is estimated from the sample, whereas a Z-test is used when the population variance is known.

Question 12

A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63.
-The t score is

Accepted Answer

The t score formula is (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). In this case, the sample mean is 40, the population mean is 35, the sample standard deviation is 7 and the sample size is not given. However, we are given the standard deviation of the distribution of means, which is 1.63. This suggests that the sample size is large enough to use the normal distribution approximation of the t-distribution. Using the formula, we get t = (40-35) / (1.63) = 3.07. Therefore, the best choice is B.

Question 13

In a t test for dependent means,15 participants are each tested twice.This makes a total of 15 "before" scores and 15 "after" scores.What are the degrees of freedom?

Accepted Answer

The degrees of freedom for a t-test for dependent means is calculated as the number of pairs minus one. Since there are 15 participants each tested twice, there are 15 pairs of scores, making the degrees of freedom 15 - 1 = 14.

Question 14

A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4.
-The psychologist tests the null hypothesis that the level of depression of fourth graders in this class does not differ from fourth graders in general at the school and obtains a t score of -0.20.The decision regarding the null hypothesis would be to

Accepted Answer

Since the t score obtained is not statistically significant, we fail to reject the null hypothesis. Therefore, there is no evidence to suggest that the level of depression in fourth graders in this class differs from that of fourth graders in general at the school.

Question 15

If a sample includes three individuals with scores of 4,6,and 8,the estimated population variance is

Accepted Answer

The estimated population variance uses the formula for sample variance: sum of squared deviations from the mean divided by (n-1). Here, the mean is 6, deviations are 2, 0, and 2, squared deviations are 4, 0, and 4. Sum is 8, divided by (3-1) = 2, giving 4.

Question 16

A school psychologist is using a depression inventory—on which a score of 0 indicates no depression and a score of 10 indicates severe depression—to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school. The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale, but the variation is unknown. The current sample of 20 fifth graders has a mean depression score of 4.4.
-If the unbiased estimate of the population's variance is 15,the variance of the distribution of means is

Accepted Answer

The variance of the distribution of means, also known as the standard error of the mean squared, is calculated by dividing the population variance by the sample size. Here, the population variance is given as 15, and the sample size is 20, so the variance of the distribution of means is 15 / 20 = 0.75.

Question 17

A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63.
-If there were 30 students in the class and the professor wanted to test the null hypothesis described in the scenario using the 5% level of significance,the cutoff t score would be

Accepted Answer

The cutoff t score for a one-tailed test at the 5% level of significance with 29 degrees of freedom (n-1, where n is the sample size of 30) is approximately 1.699. This value is used to determine if the sample mean significantly differs from the population mean under the null hypothesis.

Question 18

Which of the following statements about degrees of freedom is TRUE?

Accepted Answer

Degrees of freedom refers to the number of scores in a sample that are free to vary. It is calculated as N - 1, where N is the sample size. Option A is incorrect because N - 2 refers to a specific formula for calculating t-scores in a dependent samples t-test. Option C is partially correct in that degrees of freedom are used in effect size calculations, but this is not their primary purpose. Option D is incorrect because degrees of freedom do not increase bias in statistical estimates.

Question 19

A professor believes the students in a statistics class this term are more creative than most other students attending the university. A previous study found that students at the university had a mean score of 35 on a standard creativity test, and the current class has an average score of 40 on this scale with an estimated population standard deviation of 7. The standard deviation of the distribution of means is 1.63.
-The effect size is

Accepted Answer

The answer of A professor believes the students in a...

Question 20

When estimating the variance of a population from the sample,the sample variance cannot be used directly because

Accepted Answer

The items below (# 10 - 12)are based on the following scenario. A school psychologist is using a depression inventory-on which a score of 0 indicates no depression and a score of 10 indicates severe depression-to see if the level of depression in fourth graders in a particular class of 20 students differs from that of fourth graders in general at a school.The results of previous testing indicate that fourth graders at the school usually have a score of 5 on the scale,but the variation is unknown.The current sample of 20 fifth graders has a mean depression score of 4.4.

Quiz 7: Introduction to T Tests: Single Sample and Dependent Means