MATH 110 Exam 8 Statistics Questions and
Answers- Portage Learning
1. . Independent random samples were selected from population 1 and population 2. The
p p p p p p p p p p p p
following information was obtained from these samples:
p p p p p p p
a) Find the 95% confidence interval for estimating the difference in the population means(µ -
p p p p p p p p p p p p p p 1pp p
µ ).
p 2
Solution. When we look back at table 6.1, we see that 95% confidence corresponds to z=1.96.
p p p p p p p p p p p p p p p
a) Notice that the sample sizes are each greater than 30, so we may use eqn. 8.1:
p p p p p p p p p p p p p p p
b) Notice that the 95% confidence interval covers both positive and negative values. Therefore,we
p p p p p p p p p p p p p
cannot be 95% confident that there is a difference in the two population means.
p p p p p p p p p p p p p p
2. 2. A company would like to determine if there is a difference in the number of days that
p p p p p p p p p p p p p p p p p
employees are absent from the East Side Plant compared to the West Side Plant. So, the
p p p p p p p p p p p p p p p p
company takes a sample of 54 employees from the East Side Plant and finds that these
p p p p p p p p p p p p p p p p
people missed an average of 5.3 days last year with a standard deviation of 1.3 days. A
p p p p p p p p p p p p p p p p p
sample of 41 employees from the West Side plant revealed that these people were absentan
p p p p p p p p p p p p p p p p
average of 6.8 days last year with a standard deviation of 1.8 days.
p p p p p p p p p p p p p
a) Find the 96% confidence interval for estimating the difference in the population means(µ -
p p p p p p p p p p p p p p 1pp p
µ ).
p 2
Solution. When we look back at table 6.1, we see that 96% confidence corresponds to z=2.05.If we
p p p p p p p p p p p p p p p p p
say that the East Side Plant corresponds to population 1 and the West Side Plant corresponds to
p p p p p p p p p p p p p p p p p
population 2, then:
p p p
n =54, n =41, s =1.3, s =1.8, xぁ= 5.3, x あ= 6.8,
1 p 2 p 1 p 2 p p p p p p p p
a) We will use eqn. 8.1:p p p p
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p p p p p p p p p p p p p
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, b) Notice that the entire 96% confidence interval is negative (it is never positive or zero). Therefore,
p p p p p p p p p p p p p p p
we can say that we are 96% confident that there is a difference in the two populationmeans.
p p p p p p p p p p p p p p p p p p
c) Since the entire confidence interval is negative, we can be 96% confident that (µ1 - µ2) is
p p p p p p p p p p p p p p p p
negative. This means that on average, people from the West Side Plant will be absent more
p p p p p p p p p p p p p p p p
days than people from the East Side Plant..
p p p p p p p p
3. The mayor of a city would like to know if there is a difference in the systolic blood
p p p p p p p p p p p p p p p p p
pressure of those who live in her city compared to those who live in the rural area outside
p p p p p p p p p p p p p p p p p p
the city. So, 77 city dwellers are selected and it is found that their mean systolic blood
p p p p p p p p p p p p p p p p p
pressure is 142 with a standard deviation of 10.7. Also, 65 people are selected fromthe
p p p p p p p p p p p p p p p p
surrounding rural area and it is found that their mean systolic blood pressure is 129 with a
p p p p p p p p p p p p p p p p p
standard deviation of 8.6.
p p p p
a) Find the 98% confidence interval for estimating the difference in the population means(µ -
p p p p p p p p p p p p p p 1pp p
µ ).
p 2
Solution. When we look back at table 6.1, we see that 98% confidence corresponds to z=2.33.If we
p p p p p p p p p p p p p p p p p
say that the city residents corresponds to population 1 and the rural corresponds to population 2,
p p p p p p p p p p p p p p p p
then:
p
n =77, n =65, s =10.7, s =8.6, x̄ = 142, x̄ = 129
1 p 2 p 1 p 2 p 1pp p p p 2pp p p
a) We will use eqn. 8.1: p p p p
b) Notice that the entire 98% confidence interval is positive (it is never negative or zero). Therefore,
p p p p p p p p p p p p p p p
p we can say that we are 98% confident that there is a difference in the two populationmeans.
p p p p p p p p p p p p p p p p p
c) Since the entire confidence interval is positive, we can be 98% confident that (µ1 - µ2) is
p p p p p p p p p p p p p p p p
positive. This means that on average, people from the city have higher systolic blood pressure
p p p p p p p p p p p p p p p
than those from the rural area.
p p p p p p
Problem Set 8.2 Solutions p p p
1. Suppose we have independent random samples of size n = 780 and n = 700. The
p p p p p p p p p 1pp p p p p 2ppp p p
number of successes in the two samples were x = 538 and x = 434. Find the 95%
p p p p p p p p p 1 p p p 2ppp p p p p
confidence interval for the difference in the two population proportions. Solution. From
p p p p p p p p p p p p
table 6.1, we see that 95% confidence corresponds to z=1.96.
p p p p p p p p p p
Recall p = x /n = 538/780= .6897 and p = x /n = 434/700= .62.
p 1pp p p 1 1pp p p p p p 2pp p p 2 2pp p p p
Notice that the sample sizes are each greater than 30, so we may use eqn. 8.2:
p p p p p p p p p p p p p p p
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pk pk pk pk pk pk pk pk pk pk pk pk pk
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Answers- Portage Learning
1. . Independent random samples were selected from population 1 and population 2. The
p p p p p p p p p p p p
following information was obtained from these samples:
p p p p p p p
a) Find the 95% confidence interval for estimating the difference in the population means(µ -
p p p p p p p p p p p p p p 1pp p
µ ).
p 2
Solution. When we look back at table 6.1, we see that 95% confidence corresponds to z=1.96.
p p p p p p p p p p p p p p p
a) Notice that the sample sizes are each greater than 30, so we may use eqn. 8.1:
p p p p p p p p p p p p p p p
b) Notice that the 95% confidence interval covers both positive and negative values. Therefore,we
p p p p p p p p p p p p p
cannot be 95% confident that there is a difference in the two population means.
p p p p p p p p p p p p p p
2. 2. A company would like to determine if there is a difference in the number of days that
p p p p p p p p p p p p p p p p p
employees are absent from the East Side Plant compared to the West Side Plant. So, the
p p p p p p p p p p p p p p p p
company takes a sample of 54 employees from the East Side Plant and finds that these
p p p p p p p p p p p p p p p p
people missed an average of 5.3 days last year with a standard deviation of 1.3 days. A
p p p p p p p p p p p p p p p p p
sample of 41 employees from the West Side plant revealed that these people were absentan
p p p p p p p p p p p p p p p p
average of 6.8 days last year with a standard deviation of 1.8 days.
p p p p p p p p p p p p p
a) Find the 96% confidence interval for estimating the difference in the population means(µ -
p p p p p p p p p p p p p p 1pp p
µ ).
p 2
Solution. When we look back at table 6.1, we see that 96% confidence corresponds to z=2.05.If we
p p p p p p p p p p p p p p p p p
say that the East Side Plant corresponds to population 1 and the West Side Plant corresponds to
p p p p p p p p p p p p p p p p p
population 2, then:
p p p
n =54, n =41, s =1.3, s =1.8, xぁ= 5.3, x あ= 6.8,
1 p 2 p 1 p 2 p p p p p p p p
a) We will use eqn. 8.1:p p p p
This study source was downloaded by 100000848594376 from CourseHero.com on 01-16-2023 21:26:16 GMT -06:00
p p p p p p p p p p p p p
https://www.coursehero.com/file/81393958/MATH-110-Module-8-ANSWERSdocx/
, b) Notice that the entire 96% confidence interval is negative (it is never positive or zero). Therefore,
p p p p p p p p p p p p p p p
we can say that we are 96% confident that there is a difference in the two populationmeans.
p p p p p p p p p p p p p p p p p p
c) Since the entire confidence interval is negative, we can be 96% confident that (µ1 - µ2) is
p p p p p p p p p p p p p p p p
negative. This means that on average, people from the West Side Plant will be absent more
p p p p p p p p p p p p p p p p
days than people from the East Side Plant..
p p p p p p p p
3. The mayor of a city would like to know if there is a difference in the systolic blood
p p p p p p p p p p p p p p p p p
pressure of those who live in her city compared to those who live in the rural area outside
p p p p p p p p p p p p p p p p p p
the city. So, 77 city dwellers are selected and it is found that their mean systolic blood
p p p p p p p p p p p p p p p p p
pressure is 142 with a standard deviation of 10.7. Also, 65 people are selected fromthe
p p p p p p p p p p p p p p p p
surrounding rural area and it is found that their mean systolic blood pressure is 129 with a
p p p p p p p p p p p p p p p p p
standard deviation of 8.6.
p p p p
a) Find the 98% confidence interval for estimating the difference in the population means(µ -
p p p p p p p p p p p p p p 1pp p
µ ).
p 2
Solution. When we look back at table 6.1, we see that 98% confidence corresponds to z=2.33.If we
p p p p p p p p p p p p p p p p p
say that the city residents corresponds to population 1 and the rural corresponds to population 2,
p p p p p p p p p p p p p p p p
then:
p
n =77, n =65, s =10.7, s =8.6, x̄ = 142, x̄ = 129
1 p 2 p 1 p 2 p 1pp p p p 2pp p p
a) We will use eqn. 8.1: p p p p
b) Notice that the entire 98% confidence interval is positive (it is never negative or zero). Therefore,
p p p p p p p p p p p p p p p
p we can say that we are 98% confident that there is a difference in the two populationmeans.
p p p p p p p p p p p p p p p p p
c) Since the entire confidence interval is positive, we can be 98% confident that (µ1 - µ2) is
p p p p p p p p p p p p p p p p
positive. This means that on average, people from the city have higher systolic blood pressure
p p p p p p p p p p p p p p p
than those from the rural area.
p p p p p p
Problem Set 8.2 Solutions p p p
1. Suppose we have independent random samples of size n = 780 and n = 700. The
p p p p p p p p p 1pp p p p p 2ppp p p
number of successes in the two samples were x = 538 and x = 434. Find the 95%
p p p p p p p p p 1 p p p 2ppp p p p p
confidence interval for the difference in the two population proportions. Solution. From
p p p p p p p p p p p p
table 6.1, we see that 95% confidence corresponds to z=1.96.
p p p p p p p p p p
Recall p = x /n = 538/780= .6897 and p = x /n = 434/700= .62.
p 1pp p p 1 1pp p p p p p 2pp p p 2 2pp p p p
Notice that the sample sizes are each greater than 30, so we may use eqn. 8.2:
p p p p p p p p p p p p p p p
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pk pk pk pk pk pk pk pk pk pk pk pk pk
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