Q: A test has a mean of 50 and a standard deviation of 10. What raw score corresponds to a z-score of -1.5?

$$X = 50 + (-1.5 \times 10) = 35$$

Question 1

A researcher wants to know if a new drug affects reaction time. She collects data from a sample and calculates a z-score of 2.5. If the test is two-tailed and the alpha level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis because the z-score exceeds the critical value ($$z_{critical} = \pm 1.96).$$

Question 2

Which formula correctly transforms a raw score $$X$$ into a z-score?

Accepted Answer

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

Question 3

A population has a mean of 100 and a standard deviation of 15. What is the z-score for a test score of 130?

Accepted Answer

$$z = 2.0$$

Question 4

If you want to be among the top 20% of a population on a test, what is the minimum z-score you need?

Accepted Answer

$$z = 0.84$$

Question 5

Which of the following statements about standard error is correct?

Accepted Answer

Standard error decreases as sample size increases.

Question 6

A psychologist tests whether people type faster on a new keyboard. The null hypothesis is that there is no difference in typing speed. If the calculated z-score is $$z = 2.98$$ and the critical value for a two-tailed test at $$\alpha = 0.01 is$$ $$z_{critical} = \pm 2.58$$, what should the psychologist conclude?

Accepted Answer

Reject the null hypothesis; there is a significant difference in typing speed.

Question 7

Which of the following is NOT a factor in the Central Limit Theorem?

Accepted Answer

The sample median

Question 8

Given a sample mean of 120, a population mean of 100, and a standard deviation of 10, what is the z-score for the sample mean?

Accepted Answer

$$z = 2.0$$

Question 9

If the alpha level is $$\alpha = 0.05$$ and you are conducting a one-tailed test, what is the critical z-value?

Accepted Answer

$$z_{critical} = 1.65$$

Question 10

A sample of 25 students has a mean test score of 80 and a standard deviation of 20. What is the standard error of the mean?

Accepted Answer

$$SE = \frac{20}{\sqrt{25}} = 4$$

Question 11

Which of the following alternative hypotheses is directional?

Accepted Answer

People who drink coffee will have higher test scores than those who do not.

Question 12

If you have a sample mean of 85, a population mean of 80, and a standard error of 1.5, what is the z-score?

Accepted Answer

$$z = \frac{85 - 80}{1.5} = 3.33$$

Question 13

Which of the following is the correct interpretation of a z-score of 0?

Accepted Answer

The score is equal to the mean.

Question 14

A test has a mean of 50 and a standard deviation of 10. What raw score corresponds to a z-score of -1.5?

Accepted Answer

$$X = 50 + (-1.5 	imes 10) = 35$$

Question 15

Which of the following is true about a two-tailed test?

Accepted Answer

It tests for differences in both directions from the mean.

Question 16

If the critical z-value for a two-tailed test at $$\alpha = 0.01 is$$ $$\pm 2.58$$, what is the probability of making a Type I error?

Accepted Answer

1%

Question 17

A sample of 100 people has a mean IQ of 105 and a standard deviation of 15. What proportion of people have an IQ less than 90?

Accepted Answer

About 16%

Question 18

Which of the following is NOT required to calculate a z-score?

Accepted Answer

The sample median

Question 19

If you have a z-score of 1.28, what percentile does this correspond to?

Accepted Answer

90th percentile

Question 20

A researcher wants to test if a new teaching method improves test scores. She sets $$\alpha = 0.05$$ and conducts a one-tailed test. The calculated z-score is 1.61. What is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis; the z-score does not exceed the critical value ($$z_{critical} = 1.65).$$

Statistical Concepts and Hypothesis Testing in Biology: Study Guide

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