Question 1

Which of the following best describes the difference between descriptive statistics and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize scores from a research study, while inferential statistics draw conclusions that go beyond the scores from a research study.

Question 2

A researcher wants to know if a new teaching method improves test scores. She collects scores from two groups: one taught with the new method and one with the traditional method. What statistical branch is she using to determine if the difference in scores is significant?

Accepted Answer

Inferential statistics

Question 3

In hypothesis testing, what does the null hypothesis ($$H_0) $$typically state?

Accepted Answer

There is no difference or effect between the groups being compared.

Question 4

A psychologist tests a training program to reduce stress. Previous research shows the mean stress level is $$\mu = 85$$ with $$\sigma = 15. $$After the program, a participant's stress level is $$X = 60. $$What is the $$z-$$score for this participant?

Accepted Answer

$$z = \frac{60 - 85}{15} = -1.67$$

Question 5

If a researcher uses a two-tailed test with a significance level of $$p \u003c .05$$, what is the critical $$z-$$value for rejecting the null hypothesis?

Accepted Answer

$$z = \pm 1.96$$

Question 6

Which of the following statements about Type I and Type II errors is correct?

Accepted Answer

Type I error is rejecting the null hypothesis when it is true; Type II error is failing to reject the null hypothesis when it is false.

Question 7

In a two-tailed hypothesis test at the $$p \u003c .05$$ level, what percentage of the distribution is in each tail?

Accepted Answer

2.5%

Question 8

A researcher finds a $$z-$$score of $$-1.67$$ for her sample. Using a two-tailed test at $$p \u003c .05$$, what should she conclude?

Accepted Answer

Fail to reject the null hypothesis; the result is not statistically significant.

Question 9

Which of the following is NOT a step in the hypothesis-testing process?

Accepted Answer

Calculate the mean of the sample.

Question 10

Why do researchers use inferential statistics in studies involving samples?

Accepted Answer

To make conclusions about the population based on the sample data.

Question 11

In the context of hypothesis testing, what does a 'critical value' refer to?

Accepted Answer

The value that separates the rejection region from the non-rejection region in the comparison distribution.

Question 12

A researcher sets a very strict significance level ($$p \u003c .01) $$for her study. What is a likely consequence?

Accepted Answer

The probability of a Type II error increases.

Question 13

Which formula correctly calculates a $$z-$$score for a sample value $$X$$, given population mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{X - \mu}{\sigma}$$

Question 14

In a medical study, the null hypothesis states that a new drug has no effect on blood pressure. If the study finds a statistically significant decrease in blood pressure, what does this mean?

Accepted Answer

The null hypothesis is rejected in favor of the research hypothesis.

Question 15

Which of the following best describes a two-tailed hypothesis test?

Accepted Answer

It divides the significance level between both tails of the distribution.

Question 16

A researcher calculates a $$z-$$score for her sample and finds it falls within the non-rejection region. What should she report?

Accepted Answer

There is not enough evidence to reject the null hypothesis.

Question 17

Which of the following is a consequence of decreasing the probability of a Type I error?

Accepted Answer

The probability of a Type II error increases.

Question 18

In a published research article, what does it mean if a result is reported as 'statistically significant' with $$p \u003c .05$$?

Accepted Answer

The probability of the result occurring by chance is less than 5%.

Question 19

A researcher is testing whether a new reading program affects student performance but does not predict whether scores will increase or decrease. What type of hypothesis test should be used?

Accepted Answer

Two-tailed test

Chapter 5: Introduction to Hypothesis Testing and Inferential Statistics

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