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Based on past data, it is known that about 20.5% of people smoke cigarettes. Suppose we take a sample of 100 people currently and find that only 12% smoke cigarettes. We want to see if there is evidence that the percentage of people who smoke cigarettes is decreasing. ROUND TO FOUR DECIMAL PLACES a. If I wanted to control my margin of error and set it to 3% with 99% confidence, what sample size would I need to take instead of the 100? b. Using my original sample size of 100, what would be the 99% confidence interval for the population proportion? c. What are the null and alternative hypotheses?

Based on past data, it is known that about 20.5% of people smoke cigarettes. Suppose we take a sample of 100 people currently and find that only 12% smoke cigarettes. We want to see if there is evidence that the percentage of people who smoke cigarettes is decreasing. ROUND TO FOUR DECIMAL PLACES a. If I wanted to control my margin of error and set it to 3% with 99% confidence, what sample size would I need to take instead of the 100? b. Using my original sample size of 100, what would be the 99% confidence interval for the population proportion? c. What are the null and alternative hypotheses?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Based on past data, it is known that about 20.5% of people smoke cigarettes. Suppose we take a sample of 100 people currently and find that only 12% smoke cigarettes. We want to see if there is evidence that the percentage of people who smoke cigarettes is decreasing.
ROUND TO FOUR DECIMAL PLACES
a. If I wanted to control my margin of error and set it to 3% with 99% confidence, what sample size would I need to take instead of the 100?
b. Using my original sample size of 100, what would be the 99% confidence interval for the population proportion?
c. What are the null and alternative hypotheses?
d. What is the critical value at 99% confidence?
e. Calculate the test statistic (using the sample of 100).
f. Find the p-value.
g. What conclusion would be made here at the 99% confidence level?

 

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Step 1

Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts for you. To get the remaining sub-parts solved please repost the complete question and mention the sub-parts to be solved.

a)

Margin Error, E = 0.03

z value at 99% confidence = 2.576

Find the Margin Error

Statistics homework question answer, step 1, image 1

Step 2

b)

n = 100

Calculate the Confidence Interval.

Statistics homework question answer, step 2, image 1

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