Homework 7 - Department of Psychological Sciences

PSY 201 1
Introduction to Statistics in Psychology: PSY 201
Greg Francis, PhD
Department of Psychological Sciences
Psychological Sciences Building, Room 3174
(765) 494-6934
email: gfrancis@purdue.edu
http://www1.psych.purdue.edu/∼gfrancis/Classes/PSY201/
Homework 7
Due: 08 October 2010
Hand in your answers on a separate sheet of paper.
(1) For a population with a standard deviation σ = 10, how large a sample is necessary to have a
standard error that is:
a) equal to 5?
b) equal to 2?
c) equal to 1?
(2) For a population with a mean of µ = 60 and a standard deviation of σ = 24, find the z-score
of the sampling distribution corresponding to each of the following samples.
a) X = 63 for a sample of n = 16 scores.
b) X = 63 for a sample of n = 36 scores.
c) X = 63 for a sample of n = 64 scores.
(3) The population of IQ scores forms a normal distribution with a mean of µ = 100 and a standard
deviation of σ = 15. What is the probability of obtaining a sample mean greater than X = 105,
a) for a random sample of n = 9 people?
b) for a random sample of n = 36 people?
(4) A population of scores forms a normal distribution with a mean of µ = 40 and a standard
deviation of σ = 12.
a) What is the probability of randomly selecting a score less than X = 34?
b) What is the probability of selecting a sample of n = 9 scores with a mean less than X = 34?
c) What is the probability of selecting a sample of n = 36 scores with a mean less than X = 34?

PSY 201 2
(5) People are selected to serve on juries by randomly picking names from the list of registered
voters. The average age for registered voters in the county is µ = 39.7 years with a standard
deviation of σ = 12.4. A statistician randomly selects a sample of n = 16 people who are currently
serving on juries. The average age for individuals in the sample is X = 48.9 years.
a) How likely is it to obtain a random sample of n = 16 jurors with an average age greater than
or equal to 48.9?
b) Is it reasonable to conclude that this set of n = 16 people is not a representative random
sample of registered voters?
(6) A normal-shaped distribution has µ = 80 and σ = 15.
a) Sketch the distribution of sample means for samples of n = 25 scores from this population.
b) What are the z-score values that form the boundaries of the middle 95% of the distribution
of sample means?
c) Compute the z-score for X=89 for a sample of n = 25 scores. Is this sample mean in the
middle of the 95% of the distribution?
d) Compute the z-score for X=84 for a sample of n = 25 scores. Is this sample mean in the
middle of the 95% of the distribution?