5.22. A GSS asked, "What do you think is the ideal
number of children for a family to have?' The 497
females who responded had a median of 2, mean
of 3.02, and standard deviation of 1.81.
(a) Report the point estimate of the population
mean.
(b) Find and interpret the standard error of the
sample mean.
(c) The 95% confidence interval is 2.9,3.2). Inter-
pret.
(d) Is it plausible that the population mean = 2.0?
Explain.
5.20. Find and interpret the 95% confidence interval for
u, if y = 70 and S = 10, based on a sample size of
(a) 5
(b) 20.
5.4. A national survey conducted in July 2006 by Pew
Forum on Religion & Public Life asked whether
the subject favored allowing homosexual couples
to enter into civil unions-legal agreements that
would give them many of the same rights as mar-
ried couples. Of 2003 adults interviewed, 54% said
yes, 42% said no, and 4% had no opinion. Find the
estimated standard error for the sample proportion
answering yes. Interpret it.
5.40. An estimate is needed of the mean acreage of
farms in Manitoba, Canada. The estimate should
be correct to within 100 acres with probability 0.95.
A preliminary study suggests that 500 acres is a rea-
sonable guess for the standard deviation of farm
size.
(a) How large a sample of farms is required?
(b) A random sample is selected of the size found
in (a). The sample has a standard deviation of
300 acres, rather than 500. What is the margin
of error for a 95% confidence interval for the
mean acreage of farms?
5.14. When the 2000 GSS asked whether human beings
developed from earlier species of animals (variable
SCITEST4), 53.8% of 1095 respondents answered
that this was probably or definitely not true. Find a
99% confidence interval for the corresponding pop-
ulation proportion, and indicate whether you can
conclude that a majority of Americans felt this way.
5.67. Increasing the confidence level causes the width of
a confidence interval to
(a) increase
(b) decrease
(c) stay the same.
5.68. Other things being equal, quadrupling the sample
size causes the width of a confidence interval to
(a) double
(b) halve
(c) be one quarter as wide
(d) stay the same.

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5.22
(a)
The point estimate of the population mean is 3.02.
(b)
The standard error of sample mean is given as
SE = standard deviation/sqrt(n) = 1.81/sqrt (497) = 0.081189596, it means that the standard error from mean value is 0.08119 which is a small value.
(c)
The 95% confidence interval for mean is 2.9 and 3.2, it means that the mean number of children for a family to have lies between 2.9 and 3.2....

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