adults in a recent year, 742 made a New Year's resolution to eat healthier. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence interva
adults in a recent year, 742 made a New Year's resolution to eat healthier. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence interva
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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Question
In a survey of 2104 adults in a recent year, 742 made a New Year's resolution to eat healthier.
Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
Expert Solution
Step 1
The value of z at a 90% confidence level is 1.645, which can be found by using the standard normal table.
The sample proportion is computed as follows:
The 90% confidence interval is computed as shown below:
Therefore, we are confident that the true population proportion is contained by the interval .
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