1. Suppose you flip a coin 314 times, and heads appears 159 times.(a) Construct an approximate 90% confidence interval for the probability that the coin comes upheads.(b) Approximately how many samples would you need to obtain an approximate 90% confidenceinterval with width 0.02, while keeping exactly 50.64% of flips appearing heads?(c) You give the coin to a friend, who also flips the coin 314 times, and obtains an approximateconfidence interval [0.390, 0.500] instead. What confidence level did (s) he use?

Assume that you flip a coin 314 times and heads appear 159 times.Sample size (n) is 314 andsample…

Answered: 1. Suppose you flip a coin 314 times,…

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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1. In a study of perception, 110 men are tested and 24 are found to have red/green color blindness (based on data from USA Today). Assume that this was done in a simple random manner. A 95% confidence interval estimate of the proportion of all men with red/green color blindness was found to be 0.14 to 0.30. If we learn that the actual population proportion of men with red/green colorblindness is equal to 0.12, then what can we conclude? A. The confidence interval was wrong. B. We would need to see the sample data to make any conclusions Pick either answer A or B as your answer and show your work to go with it
You sample 1O0 people to see if they have been to the grocery store in the past week, and find that 85% (.85) of them have been. What is the 95% confidence interval for this study? Leave your answer in decimal format to 2 decimal places. In other words, .04 instead of 3.6% or .11 instead of 11.4%.. O .78 to .92 .84 to .85 O .60 to 1.10 O .60 to 1.00 .15 to 1.55
In a study of the nicotine patch, 21% of those who used the patch for 2 months reported no smoking incidents in the following year. The 95% confidence interval is (17.4%, 24.8%). Which of the following is an appropriate interpretation of the 95% confidence interval? There is a 95% probability that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%. We can be 95% confident that the proportion of the sample who would report no smoking incidents in the following year is between 17.4% and 24.8%. 95% of samples will have between 17.4% and 24.8% who would report no smoking incidents in the following year. We can be 95% confident that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.
Number 12
Suppose we randomly select n=2000 Douglas College students and we find that 205 of these students are left-handed. What is the 95% confidence interval for p= the proportion of left-handed students at Douglas? Fill in the blanks (round to three decimal places): We are 95% confident that p is between and .
Suppose you didn’t know whether the coin was fair or not and you wanted to determine a 95% Confidence interval for the actual probability of obtaining a head. If you flipped the coin 16,000 times and obtained exactly 8040 heads, your 95% confidence interval would range approximately from: (a) 0.4992 to 0.5208 (b) 0.4892 to 0.5318 (c) 0.4948 to 0.5102 (d) 0.5002 to 0.5198 (e) 0.5262 to 0.5448
(5) You take a random sample from some population and form a 98% confidence interval for the population mean, a. Which quantity is guaranteed to be in the interval you form? A. 0 B. u C. D. 0.98
You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 431 randomly selected caterpillars observed, 50 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between___ and___ . b. If many groups of 431 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About____ percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about ____ percent will not contain the true population proportion.
5
If a sample of 100 people contains 15 left-handed: (a) Compute a 95% confidence interval for the proportion of left-handers in the population. (b) If we were to take a larger sample the next time we do this experiment, would we expect the confidence interval to be wider or narrower than the one in part (a)? Why? (c) If we compute a confidence interval with a higher (say 98%) confidence level for the sample in part (a), would the new confidence interval be wider or narrower than the confidence interval computed in part a)?
You are interested in constructing a 90% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 425 randomly selected caterpillars observed, 55 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all caterpillars that lived to become a butterfly is between ___and____ . b. If many groups of 425 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About ____ percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about _____percent will not contain the true population proportion.

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