1. Types of Hypothesis Tests

2. What are you testing? What are you comparing? To what are you comparing? How many?… H o :  = # One Sample-- Mean H o :  1 =  2 Two Sample-- Means H o :  = # One Sample-- Proportion H o :  1 =  2 Two Sample-- Proportions

3. One Sample Z for Mean One-Sample Mean Z Test for X  One-Sample Mean Z Test for

4. One Sample t for Mean One-Sample Mean t Test for With n-1 degrees of freedom

5. Matched Pair t Test for Difference of Means Matched Pair (Means Difference) t Test for difference of 2 samples with (n diff – 1) df

6. Two Sample t Test for Independent Samples Unpooled (assuming distributions have different variances) Two-Sample Means t Test (unpooled/separate) with df Pooled (assuming both distributions have same variance) Two-Sample Means t Test (pooled) with (n 1 + n 2 – 2) df

7. Proportions One-Sample Z Proportion Test for Two-Sample Z Proportion Test

8. How to test? 1)Read problem/situation. 2)Determine H o and H a. 3)Enter information/data into computer. 4)Read computer output (p-value). 5)Interpret results in the context of the problem/situation.

9. Example Suppose a political candidate has decided to support legalization of gambling if he is convinced that more than 2/3 of U.S. adults approve of gambling. USA Today reported the results of a Gallop poll in which 1523 adults were asked if they approved of casino gambling. The number who approved was 1035. Does the sample provide convincing evidence that more than 2/3 approve? H o :  = 2/3 and H a :  > 2/3 P-value

10. Example The Associated Press reported that a management consultant believes that, on average, workers spend 75 min/day making personal use of company technology. Suppose that the CEO of a large corporation wanted to determine whether the average amount of time spent in personal use of company technology for her employees was greater than the reported 75 minutes. Ten employees were surveyed and data entered into computer. H o :  = 75 vs. H a :  > 75 T-Test of the Mean Variable n Mean StDev SEMean t p Time 10 74.8 9.45 2.89 -.07 0.53 What conclusion should be made?

11. Example Tennis elbow: An article reported the force on the hand just after impact on a one-handed backhand drive for advanced and intermediate players. Is there evidence that the mean force for advanced players is greater than for intermediate? Adv ( n = 6, = 40.3, s = 11.3) Int ( n = 8, = 21.4, s = 8.3) H o :  A =  I vs. H a :  A >  I

12. Example DES, a nonsteroidal estrogen, was used to treat mothers until 1971 when it was banned due to its link to cervical cancer. Ten sets of brothers had their spatial thinking ability tested, where upon one brother was not exposed to the drug while in his mother’s womb and the other brother was exposed. SAMPLE: n = 10, exposed mean = 12.6, unexposed mean = 13.8 sample mean difference= -1.2, standard error of difference=.5 H o :  diff = 0 vs. H a :  diff < 0