1. Section 11.1 Inference for the Mean of a Population AP Statistics March 15, 2010 CASA

2. AP Statistics, Section 8.2.12 The t statistic The t statistic is used when we don’t know the standard deviation of the population, and instead we use the sample distribution as an estimation. The t statistic has n-1 degrees of freedom (df).

3. AP Statistics, Section 8.2.13 The t statistic The t statistic is bigger than the z statistic. We say that t distribution is a more conservative distribution. There is more area in the tails. The t statistic has n-1 degrees of freedom.

4. AP Statistics, Section 8.2.14

5. 5 The t statistic In statistical tests of significance, we still have H 0 and H a. We need to provide the mu in the calculation of the t statistic. Looking at the t table is fundamentally different than the z table.

6. AP Statistics, Section 8.2.16 Example: Mr. Young Mopping Let’s suppose that Mr. Young has been told that he should mop by 25 after 1. We collect 12 samples with an average 27.58 minutes after 1 p.m. with a standard deviation of 3.848 minutes. Is this evidence that his true mean is after 1:25?

7. AP Statistics, Section 8.2.17

8. 8

9. 9 Step 1: Mr. Young Mopping Population of interest:  Mr. Young’s mopping Parameter of interest:  average time of arrival during mopping Hypothesis  H 0 : µ=25  H a : µ>25

10. AP Statistics, Section 8.2.110 Step 2: Mr. Young Mopping We are using 1 sample t-test? Bias?  SRS not stated. Proceed with caution. Independence?  Population size is at least 10 times the sample size?  We assume that Mr. Young has done a lot of mopping Normality?  Big sample size (> 40). No  Sample is somewhat normal because the sample distribution is single peaked, no obvious outliers.

11. AP Statistics, Section 8.2.111 Step 3: Mr. Young Mopping Calculate the test statistic, and calculate the p-value.

12. AP Statistics, Section 11.112 Exercises 11.1-11.19 odd