Section 11.4 – Using Inference to make Decisions When we make a decision based upon a significance test, we hope that our conclusion is correct. But errors in judgment can occur… Type I Error Rejecting H 0 when it is in fact true. Type II Error Failing to reject H 0 when it is in fact false. These errors in decision can have profound effects on situation. Read pages 724 & 725 to see descriptions and consequences of these errors.

Section 12.1: Test about the Population Mean In most practical cases, the population standard deviation will NOT be known. In order to do a significance test, we must use the t-table again. Using the mean and standard deviation from the sample, calculate the t-statistic as you would a z-score. Using the row of the correct degrees of freedom (n-1), find the closest t-statistic within the table and read the top (“upper tail probability p ”). If H a is one sided ( ), then this is your P-value. If H a is two sided, double the result to get your P-value.

Example: H 0 :  = 5 n = 20 H a :  > 5 t = 1.81 The P-value would fall between 0.05 and (closer to 0.05). You would then compare this P-value to  and make the conclusions accordingly. H a :  <  0 H a :  >  0 H a :  ≠  0

Example: An investor in a stock portfolio worth several hundreds of dollars sued his broker because of lack of diversification which led to poor performance (low returns). The table below gives the monthly rates of returns for the 39 months that the account was managed by the broker. Comparing these returns to the population in that period, are these results compatible with the population mean of  = 0.95%?

Paired t-test Example: Do scents improve learning? 21 subjects did a pencil/paper maze while wearing a mask that was either scented or unscented. The response variable was the average time on 3 trials. Each subject worked the maze with both masks in random order. The table below is each subjects’ average times. Is there a significant difference in learning?