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The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average propor- tion of defective widgets (choose your confidence level)?

The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average propor- tion of defective widgets (choose your confidence level)?

MATLAB: An Introduction with Applications
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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3 Comparing two proportions 2 3 Comparing two proportions Two drugs are compared to find out if the outcome of one of them is better than the other, or they are essentially equivalent. The data is as follows: drug 1 drug 2 patients tested 40 patients improved 31 Set up a test with the Null Hypothesis stating that there is not a significant difference in outcome between the two. 35 25 Note As discussed in the Lecture Note on Chapter 21, since we don't have a hypothesis about the two proportion separately, we will need to use the observed proportions to set up the standard deviation. We can also use the "pooled variance" instead.
Transcribed Image Text:3 Comparing two proportions 2 3 Comparing two proportions Two drugs are compared to find out if the outcome of one of them is better than the other, or they are essentially equivalent. The data is as follows: drug 1 drug 2 patients tested 40 patients improved 31 Set up a test with the Null Hypothesis stating that there is not a significant difference in outcome between the two. 35 25 Note As discussed in the Lecture Note on Chapter 21, since we don't have a hypothesis about the two proportion separately, we will need to use the observed proportions to set up the standard deviation. We can also use the "pooled variance" instead.
1 Estimating Proportions The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average propor- tion of defective widgets (choose your confidence level)? 2 Setting Up A Test On How "Random" the Output of a Shuffling Machine Is. A gambling establishment bought a new card shuffling machine. To do a simple test for how "random” the card sequence will be after shuffling, they ran the machine a number of times, and recorded how many times an ace turned out on top of the card stack. Here are four (simulated) experiments, finding the proportion of shuffles that resulted in an ace as the first card. Since there are 4 aces in 52 cards, the theoretical probability is 4/52 = ¹/13 ≈ 0.0769 Test for this value of p, and compare the results when doing 100, 1000, and 10,000 shuffles (machines can do that). Note that all three simulations were done with the same "true" p, so representing the same shuffler. Number of shuffles Times an ace came on top 100 1000 10000 7 89 832 Note Treat these as three separate experiments, as we check how different sam- ple sizes may affect our test. Do not combine them in a single test Bonus Using the critical/acceptance region approach (rather then only stating the p-value), calculate the power, or, equivalently, the Error of Type II, as a function of one or more possible values for p (for example, p = 0.09, but feel free to choose any alternate hypothesis you like). Note that this can (and should) be done before performing the test.
Transcribed Image Text:1 Estimating Proportions The quality control people at your company have tested a sample of 450 widgets and found that 23 were defective. What is your interval estimate (confidence interval) for the average propor- tion of defective widgets (choose your confidence level)? 2 Setting Up A Test On How "Random" the Output of a Shuffling Machine Is. A gambling establishment bought a new card shuffling machine. To do a simple test for how "random” the card sequence will be after shuffling, they ran the machine a number of times, and recorded how many times an ace turned out on top of the card stack. Here are four (simulated) experiments, finding the proportion of shuffles that resulted in an ace as the first card. Since there are 4 aces in 52 cards, the theoretical probability is 4/52 = ¹/13 ≈ 0.0769 Test for this value of p, and compare the results when doing 100, 1000, and 10,000 shuffles (machines can do that). Note that all three simulations were done with the same "true" p, so representing the same shuffler. Number of shuffles Times an ace came on top 100 1000 10000 7 89 832 Note Treat these as three separate experiments, as we check how different sam- ple sizes may affect our test. Do not combine them in a single test Bonus Using the critical/acceptance region approach (rather then only stating the p-value), calculate the power, or, equivalently, the Error of Type II, as a function of one or more possible values for p (for example, p = 0.09, but feel free to choose any alternate hypothesis you like). Note that this can (and should) be done before performing the test.
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