Solution to problems chapter9
9.51
Population under study: all the adults in United States.
Survey question: should the AIDS taste be made mandatory to certain risk group /
mandatory to all
 = proportion of all those adults who said “mandatory to all”
They surveyed a sample of 1014 adults (that is n= 1014)
x = # of adults who said “mandatory to all” = 466
Sample proportion p = x/n = 466/1014
9.55
This problem consists of two sub problems
That is there are two populations are under study
Pop1 = population of all the Nonperisters
Pop2 = population of all the Persisters
n1 = size of the sample from pop1 = 44
n2 = size of the sample from pop2 = 257
x = # hours worked per week during the first quarter
1 = average # hours worked per week during the first quarter by pop1
2 = average # hours worked per week during the first quarter by pop2
a. To construct 98% confidence interval for 1 the formula is : x  z / 2 s / n
(Since sample size n1 = 44 is a large sample, we use the z- formula)
Plugging all the numbers in the formula, the interval is ( 20.558, 30.682)
Interpretation: If we draw several samples of size 44 and construct one confidence
interval corresponding to each sample, then 99% of all such constructed confidence
intervals will trap the true value of population mean.
b. similar to part a except use the values from the Persisters.
c. It is based on larger sample.
d. since the interval in part a has lower limit greater than 20, this indicates that mean
number of hours worked per week by non-persisters is greater than 20.
9.65
specified error B= 0.1 and σ = 0.8
n = (1.96 * σ/B)2
= 245. 86
Interpretation: We want to draw a sample such that we want to be 95% confidant that
error in estimation does not exceed 0.1, the size of sample should be n> 245.
9.66
Survey question: do you support 10-2 verdict in criminal cases not involving death
penalty?
N = 900 people surveyed with this questions.
71% of these 900 supported
In the whole population, the percentage of supporters (say ) is not known
Proportion of supporters inside the sample of 900 is p = .71.
To construct a 99% confidence interval for 
Step i: check if the sample size is large? Ie check if np>10 and n(1-p)>10
np = 900*.71 = 639 > 10
n(1-p) = 900*.29 =262 >10
Yes the sample size is large hence we can apply the formula
p(1  p)
Step ii : the formula is p  z / 2
n
Step iii: the computed interval is (.671, .749)
Step V: interpretation: Based on this interval we are 99% confident that the true value of
the population proportion of the supporters of the survey question fall between 67.1% and
74.9% (again our confidence is in the process of repeated sampling and not in a single
sample)