# Confidence Intervals for Population Proportions### Challenge Activity: 5.3.1 Confidence Intervals for Population Proportions#### Critical Values for Quick Reference During This Activity:| Confidence Level | Critical Value ||------------------|----------------|| 0.90 | \( z^* = 1.645 \) || 0.95 | \( z^* = 1.960 \) || 0.99 | \( z^* = 2.576 \) |---### Example Problem:A poll for a statewide election has a margin of error of 4.89 percentage points.**Question:** How many voters should be sampled for a 90% confidence interval? Round up to the nearest whole number.**Answer:** 1234 voters--- This section is part of a larger module designed to help students understand and calculate confidence intervals for population proportions effectively. The table above provides critical values associated with different confidence levels, essential for determining the sample size or margin of error in surveys and polls.

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Answered: Critical values for quick reference…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that all grade-point averages are to be standardized on a scale between 0 and 4. How many grade-point averages must be obtained so that the sample mean is within 0.005 of the population mean? Assume that a 95% range 4-0 confidence level is desired. If using the range rule of thumb, o can be estimated as =1. Does the sample size seem practical? 4 4
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.
Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4321patients treated with the drug, 148 developed the adverse reaction of nausea. Construct a 95% confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion p. ______________ (Round to three decimal) b. identify the value of the margin of error E E=______________ c. construct the confidence interval _____<p<________ d. write a statement that correctly interprets the confidence interval.
A sample mean, sample size, population standard deviation, and confidence level are provided. Use this information to complete parts (a) through (c) below. x=35, n=27, σ=5 confidence level=90% a. Use the one-mean z-interval procedure to find a confidence interval for the mean of the population from which the sample was drawn. The confidence interval is from _______ to _________. (Type integers or decimals rounded to one decimal place as needed.) b. Obtain the margin of error by taking half the length of the confidence interval. What is the length of the confidence interval? ____________ (Type an integer or decimal rounded to one decimal place as needed.) c. Obtain the margin of error by using the formula E=zα2•σn. Identify the critical value. zα2=____________ (Type an integer or decimal rounded to two decimal places as needed.) What is the margin of error obtained using the methods of parts (b) and(c)? _________ (Type an integer or decimal…
Critical values for quick reference during this activity. Confidence level Critical value 0.90 z* = 1.645 0.95 z* = 1.960 0.99 z* = 2.576 Jump to level 1 A poll for a statewide election has a margin of error of 2.22 percentage points. How many voters should be sampled for a 99% confidence interval? Round up to the nearest whole number. Ex: 1234 voters
INFERENCE FOR SINGLE POPULATION PROPORTION (CONFIDENCE INTERVAL) 11. A random sample of 400 electronic components manufactured by a certain process is tested, and 30 are found to be defective. i. Let p be the proportion of defective components. Find a 95% confidence interval for p. ii. How many components must be sampled so that the 95% confidence interval will specify the proportion of defective components to within ±0.02? Source: Statistics for Engineers and Scientists, 3rd Edition, William, C. Navidi.
Sample data set: 47 95 54 33 64 4 8 57 8 90 3 49 4 44 79 80 68 7 15 21 6 6 78 109 29 The 92% confidence interval for the population mean is <μ< place.) 9 80 48 16 40 50 . (Round answer to one decimal
Can you please help me with this question?
Determine whether the following statements are True or False: If we increase the confidence level C, then the width of the CI decreases, i.e., the CI becomes narrower. (Hint: think about what happens to the margin of error m) Suppose the mean of a population µ = 100. If we found that the margin of error is m = 2 for level of confidence 98%, then we can be 98% confident that a sample mean (computed from a sample of the same size used to compute m) is in the interval (98, 102).
Researchers studied the mean egg length (in millimeters) for a bird population. After taking a random sample of eggs, they obtained a 95% confidence interval of (45,60). What is the value of the margin of error? Choose the correct answer below. A. 15 mm B. 52.5 mm O c. 7.5 mm O D. 1.96
Critical values for quick reference during this activity. Confidence level Critical value 0.90 �∗=1.645 0.95 �∗=1.960 0.99 �∗=2.576 Jump to level 1 A poll for a statewide election has a margin of error of 1.92 percentage points. How many voters should be sampled for a 99% confidence interval? Round up to the nearest whole number. ______voters
also, what is the lower and upper limits ?

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