# 112 what are the upper and lower bounds of the 95 ci

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1.12 What are the upper and lower bounds of the 95% CI for (expressed now as a
percent) 1.13 Is the election outcome for Cameron’s party in the 95% CI? no
1.14 What statistical principle is this an example of?
Practice Quiz 3 3 Problem 2 Confidence Intervals Match the margin of error to the desired CI. Desired CI Answer Margin of Error 2.1 95% CI for a mean, 𝜎 known 5 1. ? 0.975 (?) ∗ (?√ 1 ? + (?−?̅) 2 ∑(? 𝑖 −?̅) 2 ) 2.2 80% CI for 2-sample difference in means, pooled variance 3 2. ? 0.9 (?) ∗ (√ ? 1 2 ? 1 + ? 2 2 ? 2 ) 2.3 80% CI for 2-sample difference in means, unpooled variance 2 3. ? 0.9 (?) ∗ (? ? 1 ? 1 + 1 ? 2 ) 2.4 95% prediction interval for ? ̂|? 4 4. ? 0.975 (?) ∗ (?√1 + 1 ? + (?−?̅) 2 ∑(? 𝑖 −?̅) 2 ) 2.5 95% CI for ? |? 1 5. ? 0.975 ∗ ( 𝜎 𝑋 √? )
Practice Quiz 3 4 Problem 3. Hypothesis tests 3.1 Suppose we want to test the hypothesis 0 : 0 vs. : 0 a H H 𝜎 unknown and N =50. If we want 05 . 0 We would reject the null when: 1. 0.975 (49) ( ) x t SE x 2. 05 . 0 ) ( z x SE x 3. 0.95 (50) ( ) x t SE x 4. 0.95 (49) ( ) x t SE x 3.2 Suppose we want to test the hypothesis 0 : 0 vs. : 0 a H H , 𝜎 unknown and N =100. If we want 05 . 0 We would reject the null when: 1. 0.95 (100) ( ) x t SE x 2. 0.90 (100) ( ) x t SE x 3. 0.05 (99) ( ) x t SE x 4. 0.975 (99) ( ) x t SE x 3.3 Suppose we want to test the hypothesis 0 : 1 0 H , vs 1 : 0 a H N=500 If we want 01 . 0 We would reject the null when: 1. 1 0.99 1 (499) ( ) b t SE b 2. 1 0.99 1 (500) ( ) b t SE b 3. 1 0.995 1 (498) ( ) b t SE b 4. 99 . 0 1 1 ) ( z b SE b 3.4 Suppose we want to test the hypothesis 0 : 1 0 H , vs 1 : 0 a H N=500 If we want 01 . 0 We would FAIL TO reject the null when: 1. 1 0.99 1 (500) ( ) b t SE b 2. 1 0.01 1 (498) ( ) b t SE b 3. 1 0.99 1 (499) ( ) b t SE b 4. 1 0.95 1 ( ) b z SE b
Practice Quiz 3 5 Problem 4. Inference for proportions The Department of Statistics estimates that 50% of students at the University of Washington will have taken STAT 311 by the time they graduate. You believe it is less than 50%, and decide to take a survey of graduating seniors to estimate the true proportion. Your friend gets you a list of the graduating seniors and their email addresses, and you randomly select a sample of n=200, email them, and ask them to report on a Catalyst survey whether they have taken STAT 311: 40% of seniors report that they have. Set up a 90% CI for the estimated proportion of seniors who have taken STAT 311. 4.1 Symbolic representation: ?̂ ± ? 𝛼/2 ∗ √ ?̂ (1−?̂) ? or ? = ± ? 𝛼/2 ∗ √ ?̂ (1−? ̂) ? 4.2 With plug-in values: 0.40 ± 1.64 ∗ √ 0.4(1−0.4) 200 = 0.40 ± 0.06 or [0.34, 0.46] State the null and the general alternative hypotheses. What is the approximate distribution of the sample proportion under the null hypothesis?
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