Stressed Student
03-06-2006, 12:38 AM
Here are the 3 qustions, which I need help understanding how to do them!!!
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.
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.