Ch 5:

11. A hypothetical population consists of eight individuals ages 13, 14, 17, 20, 21, 22, 24, and 30 years.

What is the probability that a person in this population is a teenager?

What is the probability of selecting a participant who is at least 20 years old?

What is the probability of selecting a participant older than 30?

15. Using the unit normal table, find the proportion under the standard normal curve that lies between each of the following:

The mean and z = 0

The mean and z = 1.96

z = 1.50 and z = 1.50

z = 0.30 and z = 0.10

z = 1.00 and z = 2.00

19. A sample of final exam scores is normally distributed with a mean equal to 20 and a variance equal to 25.

What percentage of scores is between 15 and 25?

What raw score is the cutoff for the top 10% of scores?

What is the probability of a score less than 27?

What is the proportion below 13?

21. A set of scores measuring aggression is normally distributed with a mean equal to 23 and a standard deviation equal to 2.5. Find the proportion:

To the left of x = 19.0

To the right of x = 25.5

Between the mean and x = 19.0

To the left of x = 25.5

To the right of x = 19.0

Ch 6: 17. Using the experimental sampling strategy, how many samples of size 3 (n = 3) can be drawn from a population of size:

N = 5?

N = 6?

N = 7?

N = 8?

23. A population is normally distributed with a mean of 56 and a standard deviation of 12.

What is the mean of the sampling distribution (M) for this population?

If a sample of 36 participants is selected from this population, what is the standard error of the mean (M)?

Sketch the shape of this distribution with M 3 SEM.

29. Classroom assessment: Central limit theorem. In the Ryan (2006) study described in Question 28, participants selected 120 samples of size 3 from a population of 5 scores (0, 0, 0, 3, and 6) using theoretical sampling. Based on this example,

What is the shape of the population distribution? Hint: Graph the frequency distribution of the population of scores: 0, 0, 0, 3, and 6.

What is the shape of the sampling distribution of sample means? Hint: You do not need calculations to answer this question.

31. Physical activity and enhanced mood. Williams, Dunsiger, Jennings, and Marcus (2012) conducted a study to test how enhanced mood during exercise can increase the likelihood of physical activity in the future. They reported that at 6 months of physical activity, mood scores (rated on a scale from 5 to +5) after a walking exercise were 3.3 1.2, and at 12 months, mood scores after a walking exercise were 3.3 1.3 (mean standard error). Assuming these data are normally distributed, use the steps to conduct a z transformation to determine the following probabilities:

What is the probability that a sample mean selected from this population would show no change (0) or a negative change (less than 0) at 6 months of physical activity?

What is the probability that a sample mean selected from this population would show no change (0) or a negative change (less than 0) at 12 months of physical activity?

1. A normal distribution has a mean of 10 and a standard deviation of 2. What is the z score for x=13?

2. A normal distribution has a mean of 7.5 and a variance of 4. What is the z score for x=9?

3. A normal distribution has a mean equal to 3.4? What is the probability of a score above the mean?

4. A normal distribution has a mean equal to 4.6 and a standard deviation equal to 1.4. What score is that cutoff for the top 10% of this distribution?

5. A normal distribution has a mean equal to 10 and a standard deviation equal to 1. What is the z-score cutoff for the top and bottom 2.5% of this distribution?

6. Suppose we select a sample for a population of children in which an equal number of children live with or without their biological parents. We select a sample of 50 children. What is the probability that 30 children in this sample will be children who live with their biological parents? Hint: use the normal approximation to the binomial distribution, where p and q equal.50

7. Suppose that 10% of students earn an A in a statistic course. Using this percentage, what is the probability that exactly 25 students in a random sample of 200 students will earn an A in a statistics course?

A researcher has participants read a vignette that describes a person making inappropriate remarks toward a colleague at work, and then they are asked to complete a survey. Lower total scores on the survey indicate more negative impressions of the person described in the vignette; higher total scores indicate a more positive impression. Convert the following date to z score to determine who scored above, below and the mean in this sample.

18	19	9	20
12	14	12	25
17	15	8	25
8	14	20	14
23	9	16	15
7	17	14	19
10	21	14	19
10	7	18	8
12	11	5	10
25	8	19	14