1. Assume you have administered a standardized anxiety scale to a population of

paranoid schizophrenics. The scale has μ = 50 and σ = 12. The anxiety scale scores are

not normally distributed. Suppose you sample repeatedly from this population, drawing

samples sizes of size n = 36, and construct a sampling distribution of the mean. Answer

the following questions about the sampling distribution of the mean.

a) What is the shape of the sampling distribution of the mean? Explain your answer.

b) What is the value of the mean of the sampling distribution? What is another term

(name) for this value?

c) What is the standard deviation of the sampling distribution? What is another term for

this value?

d) Make a sketch of the sampling distribution of the mean. Label the horizontal axis in

units of standard errors (standard deviations), marking off 2 standard errors on either side

of the mean.

e) Answer the following questions about the distribution of means. For each problem,

make a diagram of the distribution, shading the relevant area under the curve.

(i) What proportion of all the sample means fall between 47 and 51?

(ii) What proportion of all sample means are above 60?

(iii) What proportion of all sample means are below 47?

2. Assume that you provide are testing a drug to decrease anxiety in paranoid

schizophrenics. From above, you know that when you measure anxiety in untreated

paranoid schizophrenics, μ = 50 and σ = 12. You select a sample of 36 paranoid

schizophrenics and then administer the drug to reduce anxiety. When you measure

anxiety in this sample, the mean is 45. Conduct a two-tailed test with α = .05 to

determine if the drug significantly reduced anxiety scores in the sample. Go through

each of the steps and begin by clearly stating the hypothesis.

3. A researcher is interested in comparing a new self-paced method of teaching statistics

with the traditional method of conventional classroom instruction. On a standardized test

of knowledge of statistics, the mean score for the population of students receiving

conventional classroom instruction is μ = 60. At the beginning of the semester, she

administers a standardized test of knowledge of statistics to a random sample of 30

students in the self-paced group and finds the group mean is Mean (X with a bar over it)

= 55 and s = 14. Assume you wish to determine whether the performance for the selfpaced

group differs significantly from the performance of those students enrolled in

courses offering conventional classroom instruction.

a. State the null hypothesis.

b. Make a diagram of the regions of acceptance and rejection associated with the null

hypothesis and label the horizontal axis in terms of values of the t-statistic. Use α= .05.

c. Calculate the value of the t-statistic associated with the sample mean of X = 55.

d. Make your decision to reject and retain and describe what this means.