Question 1

The power of a statistical test can be increased by _____.

Accepted Answer

Increasing the alpha level or the sample size both increase the power of a statistical test, so "all of these" is correct.

Question 2

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What should be the critical value?

Accepted Answer

The answer of A group of 200 students takes the...

Question 3

Based on the Method of Presentation section of Chapter 8,suppose you obtained a statistically significant t value of 2.5 with 15 subjects using an alpha level of .05.How would this be reported in a psychological journal?

Accepted Answer

The correct reporting format for this scenario would be to report the degrees of freedom, which is equal to the sample size minus one (15-1 = 14) and indicate that the p-value is less than .05. Therefore, t (14) = 2.5, p < .05 is the correct option. Option A is incorrect because it incorrectly lists the t-value as less than .05, while option B is incorrect because it incorrectly lists the p-value as greater than .05. Option D is incorrect because it incorrectly reports the degrees of freedom as 15 instead of 14.

Question 4

The terms "statistically significant" and "statistically nonsignificant" are meant to apply:

Accepted Answer

The terms "statistically significant" and "statistically nonsignificant" are used to describe the result of statistical tests and do not necessarily reflect practical or real-world implications. These terms reflect the probability that the observed result occurred by chance and are not directly related to Type II errors.

Question 5

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What is the alternative hypothesis?

Accepted Answer

The alternative hypothesis should state that the students taking the Kaplan course will improve their SAT scores above the national mean of 500. The symbol ">" indicates improvement in this case. Therefore, the correct alternative hypothesis is H₁: ì > 500. Choice C is the only option that fits this description.

Question 6

A group of 200 students takes the Kaplan course in hopes that it will improve their SAT scores above the national mean of 500 on the math section.The population standard deviation of the SAT is known to be 100.Use an alpha level of .05 when answering the following questions.What is the null hypothesis?

Accepted Answer

The answer of A group of 200 students takes the...

Question 7

In general,a directional test will be _____ than a corresponding nondirectional test if the actual population mean and the hypothesized population mean differ in the specified direction.

Accepted Answer

A directional test has more power to detect a significant difference between the sample mean and the hypothesized population mean when the difference is in the specified direction. Therefore, a directional test is more likely to reject the null hypothesis and produce a significant result, making it more powerful than a corresponding nondirectional test.

Question 8

In the Applications to the Analysis of Social Problems section of Chapter 8,the confidence intervals for the mean age at which mothers think parents should talk with children about sex and the confidence intervals for the mean age at which mothers think parents should talk with children about birth control were relatively narrow.What does this mean?

Accepted Answer

Narrow confidence intervals indicate that there is a small amount of sampling error, meaning that the sample mean is likely to be very close to the population mean. This suggests a higher level of confidence in the accuracy of the sample mean. Neither A nor B are correct, as a narrow confidence interval suggests a high level of confidence in the mean, and the rejection region is not relevant for interpreting confidence intervals.

Question 9

Directional tests are often referred to as :

Accepted Answer

Directional tests are also known as one-tailed tests because they require us to predict the direction of the effect. Therefore, the best choice here is D.

Question 10

An alternative hypothesis that specifies that a population mean is different from a given value and also indicates the direction of that difference is called a:

Accepted Answer

A directional alternative hypothesis specifies not only that there is a difference between the population mean and a given value, but also indicates the direction of that difference. A differential alternative hypothesis is a broader term that simply indicates that there is a difference but does not specify the direction. Therefore, the correct answer is B, which is a directional alternative hypothesis.

Question 11

The one-sample t test is based on the assumption that:

Accepted Answer

The one-sample t test requires both the assumption that the sample is independently and randomly selected from the population of interest (a) and that the scores on the variable are normally distributed (b). Therefore, choice D is the correct answer. The assumption that the variable being studied is qualitative in nature (C) is incorrect, as the one-sample t test is used to test mean differences on a continuous variable.

Question 12

Based on the Method of Presentation section of Chapter 8,the null and alternative hypotheses should be formally written out when reporting the results of a statistical test in a psychological journal.

Accepted Answer

The answer of Based on the Method of Presentation section...

Question 13

A t value is analogous to a z score except that it represents the number of _____ a sample mean is from ì.

Accepted Answer

A t value represents the number of estimated standard errors a sample mean is from the population mean (ì).

Question 14

Which characteristics of the t distribution influences its shape?

Accepted Answer

The shape of the t-distribution is primarily influenced by the sample size. As the sample size increases, the distribution becomes more normal in shape. Other factors such as the population mean, sample mean, and size of confidence interval do not have as much effect on the shape of the t-distribution.

Question 15

When _____,and the raw scores in the population are normally distributed,then the normal and t distributions are quite _____ one another.

Accepted Answer

As per the central limit theorem, when the sample size (N) is larger than or equal to 30, the distribution of the sample mean becomes normal regardless of the shape of the population from which it is drawn. Therefore, when N > 40 and the raw scores in the population are normally distributed, the normal and t distributions are quite similar to each other.

Question 16

When we say that a test is _____ to violations of a distributional assumption,we mean that the frequency of Type I and Type II errors,and,thus,the accuracy of our conclusions,are relatively unaffected as compared to when the assumption is met.

Accepted Answer

When a test is robust to violations of a distributional assumption, it means that the test is not affected much by violations, and hence remains accurate even in such situations. Therefore, the correct choice is D(robust).

Question 17

In hypothesis testing,which of the following is assumed to be true?

Accepted Answer

In hypothesis testing, the null hypothesis is assumed to be true until there is sufficient evidence to reject it. The alternative hypothesis is the competing hypothesis to the null hypothesis, which is only accepted if there is enough evidence against the null hypothesis. Therefore, the null hypothesis is assumed to be true in hypothesis testing.

Question 18

When there is exclusive concern that the population mean differs from a value in a specified direction,we should use _____.

Accepted Answer

A directional test is appropriate when there is exclusive concern that the population mean differs from a value in a specified direction, such as being greater or less than the specified value. This type of test allows us to focus our analysis on the specific direction of interest and potentially increase the power of the test by ignoring the opposite direction. A stringent level of significance (i.e. a very low alpha level) can also be used to increase the confidence in the results. Therefore, the best choice is B) a directional test.

Question 19

Which of the following statements is an example of a two-tailed alternative hypothesis?

Accepted Answer

The answer of Which of the following statements is an...

Question 20

The critical t value needed to reject the null will always be _____ than a Z value for the same set of scores.

Accepted Answer

The critical t value is typically larger than the Z value for the same set of scores because the t-distribution accounts for additional variability in smaller sample sizes.

Quiz 8: Hypothesis Testing: Inferences About a Single Mean