Calculate the minimum sample size needed to construct a confidence interval with the desired characteristics. A researcher is looking to estimate the mean LSAT score of law school applicants who completed their undergraduate degrees at small liberal arts colleges. She wants a 99% level of confidence and maximum margin of error of 2 points. How many applicants must she survey if previous studies show the standard deviation to be approximately 9 points? As you solve the problem above showing formula and all steps, address each of the following questions. Identify the following for the problem: a) Critical Value z?/2) b) Standard Deviation ? c) Margin of Error E d) What would happen to the minimum number of applicants if you increase the standard deviation? e) What would happen to the minimum number of applicants if you increase the Margin of Error? f) What would happen to the minumum number of applicants if you utilized a lower critical value rather than 99% level of confidence?
Added by Brian F.
Close
Step 1
Identify the critical value (z-score) for a 99% confidence level: Since we want a 99% confidence level, we need to find the z-score that corresponds to the area in the middle 99% of the standard normal distribution. This leaves 1% in the tails, so we need to find Show moreā¦
Show all steps
Your feedback will help us improve your experience
Ivan Kochetkov and 84 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
Adi S.
Confidence intervals Compute the confidence intervals using StatCrunch. You may assume a normal distribution wherever necessary. For each problem, a) attach StatCrunch output, b) write a sentence of interpretation, and c) state the interval in margin of error form. 1. A sample of 25 people weighed their garbage for a year. The result was a mean of 1679.25 pounds. Assuming Ļ=300 pounds, calculate a 95% confidence interval for the mean garbage per person in the population. 2. In a sample of 200 people, 112 said they always recycle. Calculate and interpret a 95% confidence interval for the proportion of all people who always recycle. 3. A sample of ten salaries of football coaches in the NCAA is given below. Calculate a 95% confidence interval for the mean salary of all NCAA football coaches. 525000 350000 450000 618500 390000, 480900 345000 855000 304000 456500 4. In a sample of 200 students who plan to apply to Ivy League universities, the average annual family income was $143,325 with a standard deviation of $25,418. Compute a 95% confidence interval for the mean income of families with a student who plans to apply to an Ivy League university.
Lucas F.
What are the critical values ĻĀ²L and ĻĀ²R that correspond to a 98% confidence level and a sample size of 20? 8.260, 37.566 7.633, 36.191 6.844, 38.582 8.907, 32.852 Solve the problem. Find the chi-square value ĻĀ²L corresponding to a sample size of 23 and a confidence level of 90%. 12.338 33.924 1.69 16.013 Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation Ļ. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. Heights of mature White Pine trees: 99% confidence; n = 29, xĢ = 65 ft , s = 8.4 ft 8.27 ft < Ļ < 8.53 ft 4.23 ft < Ļ < 10.47 ft 6.22 ft < Ļ < 12.59 ft 5.73 ft < Ļ < 10.07 ft Solve the problem. Find the critical value ĻĀ²L corresponding to a sample size of 24 and a confidence level of 95%. 38.076 11.689 13.091 35.172
Sri K.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD