STATISTICS 9.1.
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In a survey of 2085 adults in a certain country conducted during a period of economic
uncertainty, 61% thought that wages paid to workers in industry were too low. The
margin of error was 3
Percentage points with 95%
Confidence. For parts (a) through (d) below, which represent a reasonable interpretation
of the survey results? For those that are not reasonable, explain the flaw.
(a) We are 95% confident 61%
Of adults in the country during the period of economic uncertainty felt wages paid to
workers in industry were too low.
Is the interpretation reasonable? - Answer: The interpretation is flawed. No interval has
been provided about the population proportion.
(b) We are 92% to 98% confident 61%
Of adults in the country during the period of economic uncertainty felt wages paid to
workers in industry were too low.
Is the interpretation reasonable? - Answer: A (1 -alpha) times 100%
Confidence interval constructed from (1 -alpha) times 100%
Of all simple random samples of size n from the population whose parameter is
unknown will contain the parameter. Therefore, there is a (1 -alpha) times 100%
confidence that any such interval contains the parameter.
The interpretation is flawed. The interpretation indicates that the level of confidence is
varying.
(c) We are 95% confident the proportion of adults in the country during the period of
economic uncertainty who believed wages paid to workers in industry were too low was
between 0.58 and 0.64. Is the interpretation reasonable? - Answer: The interpretation is
reasonable.
1
APPHIA - Crafted with Care and Precision for Academic Excellence.
Quality content you can rely on!
In a survey of 2085 adults in a certain country conducted during a period of economic
uncertainty, 61% thought that wages paid to workers in industry were too low. The
margin of error was 3
Percentage points with 95%
Confidence. For parts (a) through (d) below, which represent a reasonable interpretation
of the survey results? For those that are not reasonable, explain the flaw.
(a) We are 95% confident 61%
Of adults in the country during the period of economic uncertainty felt wages paid to
workers in industry were too low.
Is the interpretation reasonable? - Answer: The interpretation is flawed. No interval has
been provided about the population proportion.
(b) We are 92% to 98% confident 61%
Of adults in the country during the period of economic uncertainty felt wages paid to
workers in industry were too low.
Is the interpretation reasonable? - Answer: A (1 -alpha) times 100%
Confidence interval constructed from (1 -alpha) times 100%
Of all simple random samples of size n from the population whose parameter is
unknown will contain the parameter. Therefore, there is a (1 -alpha) times 100%
confidence that any such interval contains the parameter.
The interpretation is flawed. The interpretation indicates that the level of confidence is
varying.
(c) We are 95% confident the proportion of adults in the country during the period of
economic uncertainty who believed wages paid to workers in industry were too low was
between 0.58 and 0.64. Is the interpretation reasonable? - Answer: The interpretation is
reasonable.
1
APPHIA - Crafted with Care and Precision for Academic Excellence.
