Question
If numerous samples of N = 15 are taken from a uniform distribution and a relative frequency distribution of the means is drawn, what would
If numerous samples of N = 15 are taken from a uniform distribution and a
relative frequency distribution of the means is drawn, what would be the shape of
the frequency distribution?
8. A normal distribution has a mean of 20 and a standard deviation of 10. Two
scores are sampled randomly from the distribution and the second score is
subtracted from the first. What is the probability that the difference score will be
greater than 5? Hint: Read the Variance Sum Law section of Chapter 3.
9. What is the shape of the sampling distribution of r? In what way does the shape
depend on the size of the population correlation?
10. If you sample one number from a standard normal distribution, what is the
probability it will be 0.5?
11. A variable is normally distributed with a mean of 120 and a standard deviation
of 5. Four scores are randomly sampled. What is the probability that the mean
of the four scores is above 127?
12. The correlation between self-esteem and extraversion is .30. A sample of 84 is
taken. a. What is the probability that the correlation will be less than 0.10? b.
What is the probability that the correlation will be greater than 0.25?
13. The mean GPA for students in School A is 3.0; the mean GPA for students in
School B is 2.8. The standard deviation in both schools is 0.25. The GPAs of
both schools are normally distributed. If 9 students are randomly sampled from
each school, what is the probability that:
a. the sample mean for School A will exceed that of School B by 0.5 or more?
b. the sample mean for School B will be greater than the sample mean for
School A?
14. In a city, 70% of the people prefer Candidate A. Suppose 30 people from this
city were sampled.
a. What is the mean of the sampling distribution of p?
b. What is the standard error of p?
A population has a mean of 50 and a standard deviation of 6. (a) What are the
mean and standard deviation of the sampling distribution of the mean for N =
16? (b) What are the mean and standard deviation of the sampling distribution of
the mean for N = 20?
2. Given a test that is normally distributed with a mean of 100 and a standard
deviation of 12, find:
a. the probability that a single score drawn at random will be greater than 110
b. the probability that a sample of 25 scores will have a mean greater than 105
c. the probability that a sample of 64 scores will have a mean greater than 105
d. the probability that the mean of a sample of 16 scores will be either less than
95 or greater than 105
3. What term refers to the standard deviation of a sampling distribution?
4. (a) If the standard error of the mean is 10 for N = 12, what is the standard error
of the mean for N = 22? (b) If the standard error of the mean is 50 for N = 25,
what is it for N = 64?
5. A questionnaire is developed to assess women's and men's attitudes toward
using animals in research. One question asks whether animal research is wrong
and is answered on a 7-point scale. Assume that in the population, the mean for
women is 5, the mean for men is 4, and the standard deviation for both groups is
1.5. Assume the scores are normally distributed. If 12 women and 12 men are
selected randomly, what is the probability that the mean of the women will be
more than 2 points higher than the mean of the men?
6. If the correlation between reading achievement and math achievement in the
population of fifth graders were 0.60, what would be the probability that in a
sample of 28 students, the sample correlation coefficient would be greater than
0.65?
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