Topic 4 Exercise
Subject: Psychology / Psychological Statistics
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9.8 Specify three important properties of the sampling distribution of the
9.9 If we took a random sample of 35 subjects from some population, the
associated sampling distribution of the mean would have the following
properties (true or false).
(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
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
(b) Assume that a standard deviation, , 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, , of 21 hours describes the TV estimates for the
local population of schoolchildren. Now what can be said about the sampling
(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.
234 INTRODUCTION TO HYPOTHESIS TESTING: THE z TEST
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 mid-range 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 5 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 7–12 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
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
(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
(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)
*12.7 In Question 10.5 on page 231, 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 514.
12.8 In Review Question 11.12 on page 263, 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:
(a) Which one most strongly supports the conclusion that vitamin C increases
(b) Which one implies the largest sample size?
(c) Which one most strongly supports the conclusion that vitamin C d e creases
(d) Which one would most likely stimulate the investigator to conduct an
additional experiment using larger sample sizes?
Answers on page 514.