# Answers to 2Sample Confidence Intervals

```Answers to 2Sample Confidence Intervals
 1  Mean annual profit as % of revenue for insurance company

1.  2  Mean annual profit as % of revenue for health care company
     Difference in mean annual profit as % between insurance and health care companies
2
 1
Assumptions:
1. Independent random samples
2. App. normal (Boxplots sym)
n1 & n2< 30
x  x t
1
2
s12 s22

n1 n2
 1.304, 0.90364 
Use 2 sample T-Interval
We’re 90% confident that the mean
difference in mean annual profit as %
in insurance & health care companies
is between -1.304 and 0.90364.
Since the interval contains 0, there is
no significant difference between
them.
 1  Mean height of professional football players

2.  2  Mean height of professional basketball players
     Difference in mean height of professional football and basketball players
2
 1
Assumptions:
1. Independent random samples
2. Approximately normal
since n1 & n2>30


x1  x 2  z
s12 s22

n1 n2
 0.4146,  0.1254 
Use 2 sample Z-Interval
3.
  Mean yearly salary
 H o :   29800

 H A :   29800
Assumptions:
1. Simple random samples
2. Approximately normal
Since n > 30
We’re 95% confident that the mean
height of professional football
players is between 0.4146 and 0.1254
feet shorter than professional
Use 1 sample Z-Test
x
 8
s
n
p  value  ncdf (8, )  0
z
Reject the Ho since p-value <α.
There’s sufficient evidence to
support the claim that the mean
yearly salary is less than
\$29,800.
 1  Mean percentage of salary increase for professors at eastern colleges

4.  2  Mean percentage of salary increase for professors at western colleges
     Difference in mean % of salary increases between eastern & western colleges
2
 1
Assumptions:
1. Independent random samples
2. Approximately normal
since n1 & n2>30
Use 2 sample Z-Interval


x1  x 2  z
s12 s22

n1 n2
 0.3319, 0.93193
We’re 90% confident that the mean
% of salary increase in professor
salaries between eastern & western
colleges is between -0.3319 and
0.93193. Since the interval contains
0, there’s no significant difference.
 1  Mean weight of male wolves from Canadian Northwest Territories

5.  2  Mean weight of male wolves from Alaska
     Difference in mean weight of males wolves from Canada & Alaska
2
 1
Assumptions:
1. Independent random samples
2. App normal (Box plots sym)
since n1 & n2<30
x  x t
1
s12 s22

n1 n2
2
6.52 7.32

18
24
 98  90   2.110
 3.5, 12.5
Use 2 sample T-Interval
We’re 95% confident that the mean
weight of male wolves from Canada
are between 3.5 and 12.5 pound
heavier than the male wolves from
 1  Mean number of children in low income families

6.  2  Mean number of children in high income families
     Difference in mean number of children between low and high income families
2
 1
Assumptions:
1. Independent random samples
2. App normal (Boxplot sym)
since n1 & n2<30


s2 s2
x1  x 2  t 1  2
n1 n2
 1.314, 2.6537 
Use 2 sample T-Interval
We’re 95% confident that the mean
difference in the number of children
between low income families and
high income families is between 1.314 and 2.6537. Since the interval
contains 0, there’s no significant
difference.
 1  Mean score on reading test in the control group

7.  2  Mean score on reading test in the experimental group
     Difference in mean reading scores between control and experimental groups
2
 1
 H o : 1  2  0

 H A : 1  2  0
Assumptions:
1. Independent random samples
2. Approximately normal
since n1 & n2>30
Use 2 sample Z-Test
z
 x  x         1.552
1
2
1
2
1
2
2
2
Fail to Reject Ho since p-val >α
Insufficient evidence to support
the claim that the experimental
group scored higher.
s
s

n1 n2
p  value  0.0637
8.   mean number of days spent in the hospital
Assumptions:
1. Simple random samples
2. App normal (boxplot sym)
since n>30
Use 1 sample T-Interval
 s 
xt

 n
 6.6753, 7.898
We’re 99% confident that the mean
number of days patients spend in the
hospital is between 6.6753 and 7.898
days.
```