Homework: pg. 693 #4,6 and pg. 698#11,12 4.) A. µ=the mean gas mileage for Larry’s car on the highway Ho: µ=26 mpg Ha: µ>26 mpg B. p= the proportion of teens in your school who rarely or never fight with their friends. Ho: p=0.72 Ha: p≠0.72

Homework 6.) A. Ho and Ha have been switched. The null hypothesis should be a statement of “no change.” B. The null hypothesis should be a statement about µ, not . C. Our hypothesis should be “some claim about the population.” Whether or not it rains tomorrow is not such a statement.

Homework 11.) A. X-bar=398 B. Since the original distribution is Normal, the sampling distribution is also Normal. C. Test statistic=2.31, P-value=0.0104 D. Yes, if the mean were 354, the probability that you could get a sample mean of 398 is only 1.04%, so this is convincing evidence that mean sales are higher. 12.) A. 0.0548; B. 0.9452; C. 0.1096 398 354

Significance Tests Section 11.1 Day 2

Example pg. 690 #1 The survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students’ attitudes toward school and study habits. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to a random sample of 25 students at her college who are at least 30 years of age. Assume that scores in the population of older students are Normally distributed with a standard deviation σ=30.

Example continued… Carefully define the parameter µ in this setting. We seek evidence against the claim µ=115. What is the sampling distribution of the mean score of a sample of 25 older students if the null hypothesis is true? Make a sketch of the Normal curve of this distribution. Suppose that the sample data give . Mark this point on the axis of your sketch. If in fact, the result was . Mark this point on your sketch. Explain why one result is good evidence that the mean score of all older students is greater than 115 and why outcome is not.

Example continued… State the appropriate null and alternative hypotheses for this study. Shade the area under the curve that is the P-value for Then calculate the test statistic and the P-value. Shade differently the area under the curve that is the P-value for . Then calculate the test statistic and P-value. Explain what each of the P-values tells us about the evidence against the null hypothesis.

Example: pg. 703 #20

Carrying out significance tests Section 11.2 Day 1

Significance Level Significance Level (α) [ALPHA]- decisive level P-value is as small or smaller to reject the null Depends on what you are doing: 0.01 (more stringent) or 0.05 (usually used)

Inference Toolbox Step 1: Hypotheses Identify the population and parameter you want to draw a conclusion about. State Hypotheses OR

Step 2: Conditions SRS (or a good representation of the population) Normality: states Normality or if n<30: check histogram, needs to be roughly symmetric and no outliers, if n>30, sampling distribution will be Normal by CLT Independence: population is 10 times the sample

Step 3: Calculations Find the test statistic. Draw a sketch!!! Find the p-value

Step 4: Interpretation 3 sentences We reject/fail to reject the null hypothesis. Interpret the p-value…given a mean of _____, the probability that we found a sample mean of _____ is ______%. We have/have no evidence that….ALTERNATIVE HYPOTHESIS IN CONTEXT.

Pg. 709 #27, 29 Homework