Problem 2 confidence intervals match the margin of

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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 4 1. ? 0.9 (?) ∗ (? ? 1 ? 1 + 1 ? 2 ) 2.2 80% CI for 2-sample difference in means, pooled variance 1 2. ? 0.975 (?) ∗ (?√1 + 1 ? + (?−?̅) 2 ∑(? 𝑖 −?̅) 2 ) 2.3 80% CI for 2-sample difference in means, unpooled variance 3 3. ? 0.9 (?) ∗ (√ ? 1 2 ? 1 + ? 2 2 ? 2 ) 2.4 95% prediction interval for ? ̂|? 2 4. ? 0.975 ∗ ( 𝜎 𝑋 √? ) 2.5 95% CI for ? |? 5 5. ? 0.975 (?) ∗ (?√ 1 ? + (?−?̅) 2 ∑(? 𝑖 −?̅) 2 )
Practice Final 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. 05 . 0 ) ( z x SE x 2. 0.975 (49) ( ) x t 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 0.995 1 (498) ( ) b t SE b 3. 1 0.99 1 (500) ( ) 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 Final 5 Problem 4. Inference for proportions The Department of Statistics estimates that 35% of students at the University of Washington will have taken STAT 311 by the time they graduate. You believe it is less than 35%, 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: 30% 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: ?̂ ± ? 0.05 ∗ √ ?̂ (1−?̂) ? or ? = ± ? 0.05 ∗ √ ?̂ (1−?̂) ? 4.2 With plug-in values: 0.3 ± 1.64 ∗ √ 0.3 (1−0.3) 200 = 0.3 ± 0.05 or [0.25, 0.032] State the null and the general alternative hypotheses. What is the approximate distribution of the sample proportion under the null hypothesis? (Specify the form of the null distribution, the mean and the standard deviation, you do not need to solve for numerical value of the standard deviation). < 0.35

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