Fix the roads! ~ The Township Board of Meridian Township wants to know how much public support there is for raising property taxes to fix and maintain the roads in the township. They randomly surveyed Township residents and calculated a 90% confidence interval for the actual proportion of Meridian Township residents who are in favor of the tax increase to be (0.57, 0.62). 1. Which of the following statements must be true? A. A 99% confidence interval calculated using the same survey data will include more plausible values for the population proportion. B. If the sample size had instead been 930 residents, then the 90% confidence interval would be half as wide as the one stated above. C. If a different sample of 465 residents were to be selected, then there is a 90% chance that the new sample proportion will be between 0.57 and 0.62 2. What is the sample proportion? Give the exact answer as a decimal. ?̂=p^= 3. What is the margin of error for this confidence interval? Give the exact answer as a decimal. ??=ME= 4. What is the standard error for this confidence interval? Round your answer to 4 decimal places. ???̂=SEp^= 5. What is the 95% confidence interval using the same survey data?

Fix the roads! ~ The Township Board of Meridian Township wants to know how much public support there is for raising property taxes to fix and maintain the roads in the township. They randomly surveyed Township residents and calculated a 90% confidence interval for the actual proportion of Meridian Township residents who are in favor of the tax increase to be (0.57, 0.62). 1. Which of the following statements must be true? A. A 99% confidence interval calculated using the same survey data will include more plausible values for the population proportion. B. If the sample size had instead been 930 residents, then the 90% confidence interval would be half as wide as the one stated above. C. If a different sample of 465 residents were to be selected, then there is a 90% chance that the new sample proportion will be between 0.57 and 0.62 2. What is the sample proportion? Give the exact answer as a decimal. ?̂=p^= 3. What is the margin of error for this confidence interval? Give the exact answer as a decimal. ??=ME= 4. What is the standard error for this confidence interval? Round your answer to 4 decimal places. ???̂=SEp^= 5. What is the 95% confidence interval using the same survey data?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Question

Fix the roads! ~ The Township Board of Meridian Township wants to know how much public support there is for raising property taxes to fix and maintain the roads in the township. They randomly surveyed Township residents and calculated a 90% confidence interval for the actual proportion of Meridian Township residents who are in favor of the tax increase to be (0.57, 0.62).

1. Which of the following statements must be true?

A. A 99% confidence interval calculated using the same survey data will include more plausible values for the population proportion.
B. If the sample size had instead been 930 residents, then the 90% confidence interval would be half as wide as the one stated above.
C. If a different sample of 465 residents were to be selected, then there is a 90% chance that the new sample proportion will be between 0.57 and 0.62

2. What is the sample proportion? Give the exact answer as a decimal.

?̂=p^=

3. What is the margin of error for this confidence interval? Give the exact answer as a decimal.

??=ME=

4. What is the standard error for this confidence interval? Round your answer to 4 decimal places.

???̂=SEp^=

5. What is the 95% confidence interval using the same survey data?

( , )

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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