Problem 1
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 \(\mathrm{N}=\) \(16 ?\) (b) What are the mean and standard deviation of the sampling distribution of the mean for \(\mathrm{N}=20 ?\)
Problem 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
Problem 3
What term refers to the standard deviation of a sampling distribution?
Problem 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?
Problem 7
If numerous samples of \(\mathrm{N}=15\) 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?
Problem 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 .
Problem 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?
Problem 10
If you sample one number from a standard normal distribution, what is the probability it will be \(0.5 ?\)
Problem 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 \(127 ?\)
Problem 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?
