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2. [-12.5 Points]
DETAILS
ASWSBE14 10.E.004.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
You may need to use the appropriate appendix table or technology to answer this question.
A magazine conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service. A sample of 36 ships that carry fewer than 500 passengers resulted in an
average rating of 85.64, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.90. Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that
carry 500 or more passengers.
(a) What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?
(Use smaller cruise ships – larger cruise ships.)
(b) At 95% confidence, what is the margin of error? (Round your answer to two decimal places.)
(c) What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships? (Use smaller cruise ships – larger cruise ships. Round your answers to two decimal places.)
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3. [-/2.5 Points]
DETAILS
ASWSBE14 10.E.019.
MY NOTES
ASK
You may need to use the appropriate technology to answer this question.
Consider the following hypothesis test.
Hoimaso
Họ: Ba > 0
(a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 – Population 2.)
Population
Element
1 | 2
Difference
1
21
18
2
28
27
3
18
15
4
20
18
5
26
25
(b) Compute d.
(c) Compute the standard deviation Sg.
(d) Conduct a hypothesis test using a = 0.05.
Calculate the test statistic. (Round your answer to three decimal places.)
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
What is your conclusion?
O Reject H.
There is insufficient evidence to conclude that
ва
> 0.
O Do not Reject Ho. There is sufficient evidence to conclude that Hy > 0.
O Do not reject Ho. There is insufficient evidence to conclude that
Md
>0.
O Reject Ho. There is sufficient evidence to conclude that
Md > 0
4. [-12.5 Points]
DETAILS
ASWSBE14 10.E.020.MI.
MY NOTES
ASK YOUR TEACHER
You may need to use the appropriate appendix table or technology to answer this question.
Recall the method used to obtain a confidence interval for the difference between two population means for matched samples.
(a) The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 – Population 2.)
Population
Element
1
2.
Difference
1
11
8
2
7
8
3
9
6
4
12
7
5
13
10
6
15
15
7
15
14
(b) Compute a.
(c) Compute the standard deviation S. (Round your answer to two decimal places.)
(d) What is the point estimate of the difference between the two population means? (Use Population 1 – Population 2.)
(e) Provide a 95% confidence interval for the difference between the two population means. (Use Population 1 – Population 2. Round your answers to two decimal places.)
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5. [-/2.5 Points]
DETAILS
ASWSBE14 10.E.029.MI.SA.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
You may need to use the appropriate appendix table or technology to answer this question.
Consider the hypothesis test.
Ho: P1
P2
so
Ha: P1 – P2 > 0
The following results are for independent samples taken from the two populations.
Sample 1
Sample 2
ni
= 200
n2
= 300
P = 0.23
1
P2 =
= 0.15
(a) Calculate the test statistic. What is the p-value?
(b) With a = 0.05, what is your hypothesis testing conclusion?
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6. [-/2.5 Points]
DETAILS
ASWSBE14 10.E.043.MI.
MY NOTES
ASK YOUR TEACHER
PRACTICE ANOTHER
You may need to use the appropriate appendix table or technology to answer this question.
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair.
Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
(a) State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let P1 = population proportion most recently saying financial security more than fair and P2 = population
proportion from the year before saying financial security more than fair. Enter != for as needed.)
HO:
Hai
(b) Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
Find the value of the test statistic. (Use P1 – P2. Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
O Reject Ho. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.
O Do not reject Ho. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.
O Do not reject Ho. There is insufficient evidence to conclude the population proportions are not equal. The data do not suggest that there has been a change in the population proportion saying that their financial security is more than fair.
O Reject Ho. There is sufficient evidence to conclude the population proportions are not equal. The data suggest that there has been a change in the population proportion saying that their financial security is more than fair.
(c) What is the 95% confidence interval estimate of the difference between the two population proportions? (Round your answers to four decimal places.)
to
What is your conclusion?
The 95% confidence interval
–Select—
zero, so we can be 95% confident that the population proportion of adults saying that their financial security is more than fair (–Select—
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