William H. Knapp III

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This homework was due on Monday, October 22 at 05:00 a.m. Turkish time. Late submissions receive half credit.

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1. What is the formula for computing a z-score for a single score from a known population?

$$\frac{x}{n}$$

$$\frac{x}{\sigma}$$

$$\frac{x-\mu}{\sigma}$$

$$\frac{x-\mu}{\sigma^2}$$

$$\frac{\bar{x}-\mu}{\frac{\sigma}{n}}$$

$$\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$

2. What is the formula for computing a z-score for a mean for a sample drawn from a known population?

$$\frac{x}{n}$$

$$\frac{x}{\sigma}$$

$$\frac{x-\mu}{\sigma}$$

$$\frac{x-\mu}{\sigma^2}$$

$$\frac{\bar{x}-\mu}{\frac{\sigma}{n}}$$

$$\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$

3. Taking the z-scores for every score in some distribution, will create a standard normal distribution.
True
False

4. Taking the z-scores for every score in some distribution, will create a distribution with a mean of 0.
True
False

5. Taking the z-scores for every score in some distribution, will create a distribution with a standard deviation of 0.
True
False

6. Taking the z-scores for every score in some distribution, will create a distribution with a variance of 1.
True
False

7. If you standardize the scores, you can justifiably compare apples to oranges.
True
False

8. Imagine you are measuring cortisol levels and you find someone with a blood cortisol level of 14 micrograms per deciliter (mcg/dL). If you take the z-score of this, the z-score will also be in units of mcg/dL.
True
False

9. Let's say blood levels of cortisol are normally distributed with a mean of 9mcg/DL and a standard deviation of 2.5mcg/DL. What is the z-score for 14mcg/dL?.

10. For the previous example, let's say the null hypothesis is that the cortisol levels are at or below the mean beacuse you want to intervene if the cortisol levels are too high. In which tail(s) will our critical value(s) be?
Both tails
The lower tail
The upper tail

11. For the previous example, if we used alpha=.05, what should we do?
Fail to reject the null
Reject the null
Not enough information

12. If our null hypothesis was that cortisol levels equal to the mean, what should we have done with the same alpha level?
Fail to reject the null
Reject the null
Not enough information

13. Imagine you are friends with Paul Hunn. One day he tells you that he won a loud burping contest. He claims that his burp was 3 standard deviations beyond the average volume. He's talked about burping way too much so you know that burp volumes are normally distributed. What percent of burps are louder than his? (Hint: Use the slides and what you know about normal distributions. Also don't include the percent sign in your answer, just enter the number.)

14. Paul wants to see how smart you are and tells you the average volume for burps in burping contests are 75 decibels and that the standard deviation is 9 decibels. How loudly did he burp in the contest. (Don't include the units in your answer, just give me the number.)

15. Imagine you're a psychologist developing a new measure of extraversion. You find that your measure has a standard deviation of .2 and a mean of -.5. This is fine, but you're concerned people might feel bad if they get a negative score. Instead you want your measure to have a standard deviation of 20 and a mean of 100. Imagine someone scored a -.8 on the original measure, what would their scaled score be?

16. Imagine that after a lot of testing you determined that your scaled measure of extraversion (see above) is normally distributed. What extraversion score cuts off the top 5% of the scores? (Hint, use the value from the slides.)

17. Imagine that our university's publicist wants to market our university as friendly and outgoing and he measures a sample of 16 students with the scaled extraversion test and determines that the sample mean was 109. What z-score is this mean associated with.

18. If the publicist was using a null hypothesis that our students extraversion is less than or equal to 100 and used the traditional alpha, what should they do.
Fail to reject the null
Reject the null
Not enough information

19. What if the mean of the students was 108.
Fail to reject the null
Reject the null
Not enough information

20. What's the probability of observing a score 2.58 or more standard deviations from the mean from a normally distributed population. (Use the slides.)