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Gosset’s student-t model

Gosset’s student-t model. Part 2 Practicing with the student-t model. Student-t for Means Assumptions / conditions. Independence: data values independent – or reasonable to assume Randomization: data from random sample or randomized experiment

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Gosset’s student-t model

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  1. Gosset’s student-t model Part 2 Practicing with the student-t model.

  2. Student-t for MeansAssumptions / conditions • Independence: data values independent – or reasonable to assume • Randomization: data from random sample or randomized experiment • 10% : when we don’t have replacement, can’t sample more than 10% • Nearly normal : data come from dist. unimodal and symmetric (make histogram) - the smaller the sample the more closely it should follow a normal model Vocab A5

  3. Student-t for Means

  4. Student-t for Meansa family of distributions df = n – 1 (the family’s name) All models differ a little based on the sample size or n called degrees of freedom (df) as n approaches ∞ then t approaches normal.

  5. Student-t for MeansOne sample t-interval for the mean y ± t*n-1 SE( y ) t* look it up on the chart or use the calculator

  6. Student-t for MeansOne sample t-test for the mean the t-score

  7. Class Examples Pg 1.2- check assumptions Pg 1.3- df Pg 1.4- t* Pg 1.5- ME Pg 1.6- interval

  8. Class Examples

  9. Class Examples

  10. Class Examples f) Conduct a hypothesis test that the actual mean of the fees collected will be $130. Pg 1.7- alpha level Pg 1.8- t-value(score) Pg 1.9- p-value for the test

  11. Class Activity Testing the manufacturers claim of a certain weight in the bag. You will each be given 2 bags of fruit snacks. Each bag is marked as 22 grams in weight. You will need to weigh the contents of each bag separately and record the weight. Get the weight of each of your team mates bags and then find the mean and stdev for your tables sample. Create a 95% C.I. and do a 95% hypothesis test for your sample. See the questions on your student notes.

  12. Class Activity Testing the manufacturers claim of a certain weight in the bag. 1- What is the average and standard deviation for your tables’ sample of fruit snacks? 2- Check the assumptions and conditions of a student-t test 3- What is the df for your sample? 4- What is t* for a 95% C.I. and your sample size? 5- What is the ME for your sample? 6- What is the 95% confidence interval for your sample of fruit snacks? 7- Write your conclusion in context below. Answer Questions 2.1 through 2.10 about your sample inference.

  13. Class Activity Testing the manufacturers claim of a certain weight in the bag. 8- Write a null and alternate hypothesis for test the weight of your fruit snacks. 9- What alpha level will you use for a 95% student-t hypothesis test. 10- What is your t-score? 11- What is your p-value for the test? 12- Write your conclusion to your hypothesis test in context.

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