**Why Use an Alternative Formula for Sample Size in Confidence Intervals**When calculating the sample size required to find a confidence interval for the population proportion, you might consider using the formula \[ n \geq \frac{z_{\alpha/2}^2 \hat{p}(1 - \hat{p})}{h^2} \]instead of \[ n \geq \frac{z_{\alpha/2}^2}{4h^2} \]**Explanation:**The formula $ n \geq \frac{z_{\alpha/2}^2 \hat{p}(1 - \hat{p})}{h^2} $ allows for a more precise estimation as it incorporates the sample proportion $ \hat{p} $, making it more tailored to specific data when estimating the required sample size for a given confidence interval.- **Variables:** - $ z_{\alpha/2} $: Represents the z-score for the desired confidence level. - $ \hat{p} $: Represents the sample proportion. - $ h $: Reflects the amount of error you are willing to accept.Using this formula can provide a more accurate sample size calculation based on the actual observed data, whereas the other formula is a more general calculation that assumes maximum variability in the proportion.

when there is no prior estimate of the sample proportion () is known, then we use, putting the…

Answered: (e) Explain why you might want to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.36. You would like to be 95% confident that your esimate is within 2.5% of the true population proportion. How large of a sample size is required?
Virginia wants to estimate the percentage of students who live more than three miles from the school. She wants to create a 95% confidence interval which has a margin of error of at most 5%. How many students should be polled to create the confidence interval? z0.10 z0.05 z0.025 z0.01 z0.005 1.282 1.645 1.960 2.326 2.576 Use the table of values above.
Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $3.37 to $3.60. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.) x = $ E = $
Tina catches a 14-pound bass. She does not know the population mean or standard deviation. So she takes a sample of five friends and they say the last bass they caught was 9, 12, 13, 10, and 10 pounds. Find the t and calculate a 95% (α = .05) confidence interval.
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 55 percentage points with 90% confidence if (a) he uses a previous estimate of 28%? n=what (b) he does not use any prior estimates? n=what
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.8. You would like to be 97% confident that your esimate is within 2% of the true population proportion. How large of a sample size is required?
Abe and Betty want to estimate the mean of a population with known standard deviation o. Abe takes 50 samples whereas Betty takes 80 samples. Which of the following statements are correct? (A) If both Abe and Betty use confidence intervals of the same width, then the confidence level of Abe's interval is smaller than that of Betty's (B) If both Abe and Betty use confidence intervals of the same width, then the confidence level of Abe's interval is larger than of Betty's (C) If Abe and Betty construct confidence intervals with the same confidence level, then the width of Abe's interval is smaller than that of Betty's (D) If Abe and Betty construct confidence intervals with the same confidence level then the width of Abe's interval is larger than that of Betty's (B) and (C). (A) and (D) (B) and (D) (A) and (C)
A researcher is trying to estimate the population mean (μ) of anxiety based on his sample of n = 16 scores. His sample M = 58 and the s = 5.36. Construct the 95% confidence interval for μ.
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.34. You would like to be 90% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required
Solve the problem. An article in a journal examined the attitudes of three groups of professionals on the condition of the environment, and quantified their responses on a seven-point scale (1= no problem to 7 = disaster very likely). The mean scores for the groups are: A: 4.90 , B: 4.55 , and C: 4.51 . Using an experimentalwise error rate of a = .05, Tukey's minimum significance for comparing means is 0.29. Use this information to conduct a multiple comparisons of the means. O The lowest mean differs significantly from the other two, but there is no significant difference in the other two means. O All means are significantly different. O The highest mean differs significantly from the other two, but there is no significant difference in the other two means. O There is no significant difference in any of the means.
Beth wants to determine a 99% confidence interval for the true proportion of high school students in the area who attend their home basketball games. How large of a sample must she have to get a margin of error less than 0.04? Assume we have no prior estimate of the proportion and want a conservative choice for the sample size. n =

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS