After all necessary conditions for creating a confidence interval for a proportion were checked in a study involving a sample of randomly-selected British teenagers, a 95% confidence interval for the proportion of all British teenagers that use public transportation to travel to and from school was correctly computed to be (0.71, 0.79) when the values are reported to the nearest hundredth. Use this information to answer (a) - (d). (a) What is the statistic that was used to construct this confidence interval? Include both the statistic's symbol and value in your sentence answer. (b) What is the margin of er. r in the 95% confidence interval (0.71, 0.79)?

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1. After all necessary conditions for creating a confidence interval for a proportion were checked in a study
involving a sample of randomly-selected British teenagers, a 95% confidence interval for the proportion of
all British teenagers that use public transportation to travel to and from school was correctly computed to be
(0.71, 0.79) when the values are reported to the nearest hundredth. Use this information to answer (a) – (d).
(a) What is the statistic that was used to construct this confidence interval? Include both the statistic's
symbol and value in your sentence answer.
(b) What is the margin of er. r in the 95% confidence interval (0.71, 0.79)?
(c) In the context of this problem, dves the 95% confidence interval (0.71, 0.79) mean there's a 95%
chance that the percentage of all British teenagers that use public transportation to travel to and
from school, p, is between 71% and 79%? In other words, is P(0.71<p<0.79)=0.95 a true
statement? Why or why not? Explain clearly and completely.
(d) If the same statistic (the value you stated in your answer to part (a)), from the same sample is used
to create a 92% confidence interval, would the margin of error of this 92% confidence interval be
less than the margin of the error in the 95% confidence interval (the value you stated in your
answer to part (b))? Explain.
Transcribed Image Text:1. After all necessary conditions for creating a confidence interval for a proportion were checked in a study involving a sample of randomly-selected British teenagers, a 95% confidence interval for the proportion of all British teenagers that use public transportation to travel to and from school was correctly computed to be (0.71, 0.79) when the values are reported to the nearest hundredth. Use this information to answer (a) – (d). (a) What is the statistic that was used to construct this confidence interval? Include both the statistic's symbol and value in your sentence answer. (b) What is the margin of er. r in the 95% confidence interval (0.71, 0.79)? (c) In the context of this problem, dves the 95% confidence interval (0.71, 0.79) mean there's a 95% chance that the percentage of all British teenagers that use public transportation to travel to and from school, p, is between 71% and 79%? In other words, is P(0.71<p<0.79)=0.95 a true statement? Why or why not? Explain clearly and completely. (d) If the same statistic (the value you stated in your answer to part (a)), from the same sample is used to create a 92% confidence interval, would the margin of error of this 92% confidence interval be less than the margin of the error in the 95% confidence interval (the value you stated in your answer to part (b))? Explain.
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