Suppose a random sample of size 60 is obtained and the sample proportion is found to be 0.25. a. Find a 95% confidence for the true proportion. b. Would a 99% confidence be wider or narrower than the confidence interval found in part a? c. Suppose a sample size of 50 is obtained instead of size 60, would the resulting 95% confidence interval be narrower or wider than the confidence interval found in part a?
Added by Anthony P.
Close
Step 1
25 Sample size (n) = 60 Critical value for 95% confidence level (z) = 1.96 Margin of error (E) = z * sqrt(p-hat * (1 - p-hat) / n) E = 1.96 * sqrt(0.25 * 0.75 / 60) E = 1.96 * sqrt(0.1875 / 60) E = 1.96 * sqrt(0.003125) E = 1.96 * 0.0559 E = 0.1096 Confidence Show more…
Show all steps
Your feedback will help us improve your experience
Krishna G and 55 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The width of a confidence interval will be: A) Wider when the sample standard deviation is small than when s is large B) Narrower for 95% confidence than 99% confidence C) Narrower for 95% confidence than 90% confidence C) Wider for a sample size of 100 for a sample size of 50
Chris M.
A sample of size n = 15 has a sample mean x and a sample standard deviation s. (a) Construct a 95% confidence interval for the population mean 9bc. (b) If the sample size were n = 25 and the sample standard deviation was unchanged, would the 95% confidence interval be narrower or wider? Why? (c) Construct a 98% confidence interval for the population mean 9bc.
Adi S.
A simple random sample of size $n$ is drawn from a population that is normally distributed. The sample mean, $\bar{x},$ is found to be $108,$ and the sample standard deviation, $s,$ is found to be $10 .$ (a) Construct a $96 \%$ confidence interval about $\mu$ if the sample size, $n,$ is 25 (b) Construct a $96 \%$ confidence interval about $\mu$ if the sample size, $n,$ is $10 .$ How does decreasing the sample size affect the margin of error, $E ?$ (c) Construct a $90 \%$ confidence interval if the sample size, $n,$ is $25 .$ Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, $E ?$ (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? Why?
Estimating the Value of a Parameter Using Confidence Intervals
Confidence Intervals about a Population Mean in Practice where the Population Standard Deviation Is Unknown
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD