1. Statistics: Unlocking the Power of Data Lock 5 Section 6.6 Test for a Single Mean

2. Statistics: Unlocking the Power of Data Lock 5 Outline Test for a single mean

3. Statistics: Unlocking the Power of Data Lock 5 Chips Ahoy! ? A group of Air Force cadets bought bags of Chips Ahoy! cookies from all over the country to verify this claim. They hand counted the number of chips in 42 bags. Source: Warner, B. & Rutledge, J. (1999). “Checking the Chips Ahoy! Guarantee,” Chance, 12(1).

4. Statistics: Unlocking the Power of Data Lock 5 Chips Ahoy! Can we use hypothesis testing to prove that there are 1000 chips in every bag? (“prove” = find statistically significant) (a) Yes (b) No We can only do inference for parameters (such as mean, proportion, etc.), not for the value of every single bag.

5. Statistics: Unlocking the Power of Data Lock 5 Can we use hypothesis testing to prove that the average number of chips per bag is 1000? (“prove” = find statistically significant) (a) Yes (b) No Statements of equality are always in the null hypothesis, and we can only reject or fail or reject the null, never accept the null. Therefore, we cannot use hypothesis testing to prove equality. Chips Ahoy!

6. Statistics: Unlocking the Power of Data Lock 5 Can we use hypothesis testing to prove that the average number of chips per bag is more than 1000? (“prove” = find statistically significant) (a) Yes (b) No Chips Ahoy!

7. Statistics: Unlocking the Power of Data Lock 5 T-Test for a Single Mean If the population is approximately normal or if n is large (n ≥ 30), the p-value can be computed as the area in the tail(s) beyond t of a t-distribution with n – 1 degrees of freedom

8. Statistics: Unlocking the Power of Data Lock 5 ? Are there more than 1000 chips in each bag, on average? (a) Yes (b) No (c) Cannot tell from this data Chips Ahoy!

9. Statistics: Unlocking the Power of Data Lock 5 Chips Ahoy! This provides extremely strong evidence that the average number of chips per bag of Chips Ahoy! cookies is greater than 1000. 1. State hypotheses: 2. Check conditions: 5. Calculate test statistic: 6. Compute p-value: 7. Interpret in context: H 0 :  = 1000 H a :  > 1000 n = 42 ≥ 30 t with 42 – 1 = 41 df, upper tail p-value  0 3. Calculate statistic: 4. Calculate standard error: