PSY 520 Grand Canyon University Sampling Distribution of The Mean Worksheet Topic 4 Exercises Complete the following exercises located at the end of each c

PSY 520 Grand Canyon University Sampling Distribution of The Mean Worksheet Topic 4 Exercises Complete the following exercises located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor. Show all relevant work; use the equation editor in Microsoft Word when necessary. Chapter 9, numbers 9.7, 9.8, 9.9, 9.13, and 9.14 Chapter 10, numbers 10.9, 10.10, 10.11, and 10.12 Chapter 11, numbers 11.11, 11.19, and 11.20 Chapter 12, numbers 12.7, 12.8, and 12.10 Topic 4 Exercises
Complete the following exercises located at the end of each chapter and put them into a
Word document to be submitted as directed by the instructor.
Show all relevant work; use the equation editor in Microsoft Word when necessary.
Chapter 9, numbers 9.7, 9.8, 9.9, 9.13, and 9.14
Chapter 10, numbers 10.9, 10.10, 10.11, and 10.12
Chapter 11, numbers 11.11, 11.19, and 11.20
Chapter 12, numbers 12.7, 12.8, and 12.10
Ch.9
9.7 Define the sampling distribution of the mean.
9.8 Specify three important properties of the sampling distribution of the mean.
9.9 Indicate whether the following statements are true or false. If we took a random
sample of 35 subjects from some population, the associated sampling distribution of
the mean would have the following properties:
(a) Shape would approximate a normal curve.
(b) Mean would equal the one sample mean.
(c) Shape would approximate the shape of the population.
(d) Compared to the population variability, the variability would be reduced by a factor
equal to the square root of 35.
(e) Mean would equal the population mean.
(f) Variability would equal the population variability.
9.13 Given a sample size of 36, how large does the population standard deviation have to
be in order for the standard error to be
(a) 1 ?
(b) 2 ?
(c) 5 ?
(d) 100 ?
9.14 (a) A random sample of size 144 is taken from the local population of grade-school
children. Each child estimates the number of hours per week spent watching TV. At
this point, what can be said about the sampling distribution?
(b) Assume that a standard deviation, σ, of 8 hours describes the TV estimates for the
local population of schoolchildren. At this point, what can be said about the sampling
distribution?
(c) Assume that a mean, μ, of 21 hours describes the TV estimates for the local population
of schoolchildren. Now what can be said about the sampling distribution?
(d) Roughly speaking, the sample means in the sampling distribution should deviate, on
average, about ___ hours from the mean of the sampling distribution and from the
mean of the population.
(e) About 95 percent of the sample means in this sampling distribution should be
between ___ hours and ___ hours.
Ch.10
10.9 The normal range for a widely accepted measure of body size, the body mass index
(BMI), ranges from 18.5 to 25. Using the midrange BMI score of 21.75 as the null
hypothesized value for the population mean, test this hypothesis at the .01 level of
significance given a random sample of 30 weight-watcher participants who show a
mean BMI = 22.2 and a standard deviation of 3.1.
10.10 Let’s assume that, over the years, a paper and pencil test of anxiety yields a mean
score of 35 for all incoming college freshmen. We wish to determine whether the
scores of a random sample of 20 new freshmen, with a mean of 30 and a standard
deviation of 10, can be viewed as coming from this population. Test at the .05 level
of significance.
10.11 According to the California Educational Code
(http://www.cde.ca.gov/ls/fa/sf/peguidemidhi.
asp), students in grades 7 through 12 should receive 400 minutes of physical
education every 10 school days. A random sample of 48 students has a mean of
385 minutes and a standard deviation of 53 minutes. Test the hypothesis at the .05
level of significance that the sampled population satisfies the requirement.
10.12 According to a 2009 survey based on the United States census (http://www.census.
gov/prod/2011pubs/acs-15.pdf), the daily one-way commute time of U.S. workers
averages 25 minutes with, we’ll assume, a standard deviation of 13 minutes. An
investigator wishes to determine whether the national average describes the mean
commute time for all workers in the Chicago area. Commute times are obtained for
a random sample of 169 workers from this area, and the mean time is found to be
22.5 minutes. Test the null hypothesis at the .05 level of significance.
Ch.11
11.11 Give two reasons why the research hypothesis is not tested directly.
11.19 How should a projected hypothesis test be modified if you’re particularly concerned
about
(a) the type I error?
(b) the type II error?
11.20 Consult the power curves in Figure 11.7 to estimate the approximate detection rate,
rounded to the nearest tenth, for each of the following situations:
(a) a four-point effect, with a sample size of 13
(b) a ten-point effect, with a sample size of 29
(c) a seven-point effect with a sample size of 18 (Interpolate)
Ch.12
12.7 In Question 10.5 on page 191, it was concluded that, the mean salary among the
population of female members of the American Psychological Association is less
than that ($82,500) for all comparable members who have a doctorate and teach full
time.
(a) Given a population standard deviation of $6,000 and a sample mean salary of
$80,100 for a random sample of 100 female members, construct a 99 percent confidence
interval for the mean salary for all female members.
(b) Given this confidence interval, is there any consistent evidence that the mean salary
for all female members falls below $82,500, the mean salary for all members?
Answers on page 435.
12.8 In Review Question 11.12 on page 218, instead of testing a hypothesis, you might
prefer to construct a confidence interval for the mean weight of all 2-pound boxes of
candy during a recent production shift.
12.10 Imagine that one of the following 95 percent confidence intervals estimates the
effect of vitamin C on IQ scores:
95% CONFIDENCE INTERVAL
LOWER LIMIT
UPPER LIMIT
1
100
102
2
95
99
3
102
106
4
90
111
5
91
98
(a) Which one most strongly supports the conclusion that vitamin C increases IQ scores?
Copyright © 2017 John Wiley & Sons, Inc.
232 ESTIMATION (CONFIDENCE INTERVALS)
(b) Which one implies the largest sample size?
(c) Which one most strongly supports the conclusion that vitamin C decreases IQ
scores?
(d) Which one would most likely stimulate the investigator to conduct an additional
experiment using larger sample sizes?
Answers on page 436.

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