statistics: unlocking the power of data lock 5 section 6.2 confidence interval for a single...
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Statistics: Unlocking the Power of Data Lock5
Section 6.2
Confidence Interval for a Single Proportion
Statistics: Unlocking the Power of Data Lock5
OutlineConfidence interval for a single proportion
Determining sample size
Statistics: Unlocking the Power of Data Lock5
SE for
The standard error for is
Problem: when doing inference, we don’t know p!
Solution: substitute , our best guess for p
Statistics: Unlocking the Power of Data Lock5
Confidence Interval for p
If n is large enough for np ≥ 10 and n(1 – p) ≥ 10, then a confidence
interval for p can be computed by
*
statistic z* SE
Statistics: Unlocking the Power of Data Lock5
In March 2011, a random sample of 1000 US adults were asked
“Do you favor or oppose ‘sin taxes’ on soda and junk food?”
320 adults responded in favor of sin taxes.
Give a 95% CI for the proportion of all US adults that favor these sin taxes.
Sin Taxes
Statistics: Unlocking the Power of Data Lock5
Counts are greater than 10 in each category
For a 95% confidence interval, z* = 1.96
Sin Taxes
We are 95% confident that between 29.1% and 34.9% of US adults favor sin taxes on soda and junk food.
*
0.32
0.32 0.015
(0.291, 0.349)
Statistics: Unlocking the Power of Data Lock5
Sin Taxes
Statistics: Unlocking the Power of Data Lock5
In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the sample proportion?
A. 280B. 500C. 56D. 0.56E. 1.96
Statistics: Unlocking the Power of Data Lock5
In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the value of z*?
A. 0.56B. 1.28C. 1.645D. 1.96E. 2.576
Statistics: Unlocking the Power of Data Lock5
In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the standard error?
A. 0.56B. 500C. 0.00049D. 0.0365E. 0.0222
=0.0222
Statistics: Unlocking the Power of Data Lock5
In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the margin of error?
A. 0.56B. 500C. 0.00049D. 0.0365E. 0.0222
CI = statistic margin of error
Statistics: Unlocking the Power of Data Lock5
Margin of Error
For a single proportion, what is the margin of error?
a) b) * c) 2 *
CI = statistic margin of error
CI: *
Statistics: Unlocking the Power of Data Lock5
Margin of Error
You can choose your sample size in advance, depending on your desired margin of error!
Given this formula for margin of error, solve for n.
ME = *
Statistics: Unlocking the Power of Data Lock5
Margin of Error
n
• Neither p nor is known in advance. To be conservative, use p = 0.5.
• For a 95% confidence interval, z* 2
Statistics: Unlocking the Power of Data Lock5
Margin of Error
Suppose we want to estimate a proportion with a margin of error of 0.03 with 95% confidence.
How large a sample size do we need?
(a) About 100(b) About 500(c) About 1000(d) About 5000
n
n
Statistics: Unlocking the Power of Data Lock5
Tongue Curling
What proportion of people can roll their tongue?
Can you roll your tongue? (a) Yes (b) No Visualize and summarize the data. What is your
point estimate? Give and interpret a confidence interval. Tongue rolling has been said to be a dominant trait,
in which case theoretically 75% of all people should be able to roll their tongues. Do our data provide evidence otherwise?
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