Siblings Mary and David are each attempting to estimate the proportion of families in their neighborhood who have five or more children. Mary selects a random sample of 50 families to survey, and she observes a sample proportion of 0.10. David selects a random sample of 100 families to survey, and he also observes a sample proportion of 0.10. Mary and David each use their sample data to construct a 95% confidence interval. Who will have the more narrow confidence interval? A. Both intervals will have the same width since the sample proportions are the same. B. Both intervals will have the same width since the level of confidence is the same for each interval. C. Both intervals will have the same width since the sample proportions are the same and the level of confidence is the same for each interval. D. Mary's interval will be more narrow than David's interval.

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Siblings Mary and David are each attempting to estimate the proportion of families in
their neighborhood who have five or more children. Mary selects a random sample of 50
families to survey, and she observes a sample proportion of 0.10. David selects a random
sample of 100 families to survey, and he also observes a sample proportion of 0.10.
Mary and David each use their sample data to construct a 95% confidence interval. Who
will have the more narrow confidence interval?
A. Both intervals will have the same width since the sample proportions are the
same.
B. Both intervals will have the same width since the level of confidence is the same
for each interval.
C. Both intervals will have the same width since the sample proportions are the same
and the level of confidence is the same for each interval.
D. Mary's interval will be more narrow than David's interval.
E. David's interval will be more narrow than Mary's interval.
Transcribed Image Text:Siblings Mary and David are each attempting to estimate the proportion of families in their neighborhood who have five or more children. Mary selects a random sample of 50 families to survey, and she observes a sample proportion of 0.10. David selects a random sample of 100 families to survey, and he also observes a sample proportion of 0.10. Mary and David each use their sample data to construct a 95% confidence interval. Who will have the more narrow confidence interval? A. Both intervals will have the same width since the sample proportions are the same. B. Both intervals will have the same width since the level of confidence is the same for each interval. C. Both intervals will have the same width since the sample proportions are the same and the level of confidence is the same for each interval. D. Mary's interval will be more narrow than David's interval. E. David's interval will be more narrow than Mary's interval.
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