Chapter 9 Hypothesis Testing

Properties of the t Distribution The t distribution is different for different values of n, the sample size.

Properties of the t Distribution The t distribution is different for different values of n, the sample size. 2. The t distribution is centered at 0 and is symmetric about 0.

Properties of the t Distribution The t distribution is different for different values of n, the sample size. 2. The t distribution is centered at 0 and is symmetric about 0. 3. The area under the curve is 1. Because of the symmetry, the area under the curve to the right of 0 equals the area under the curve to the left of 0 equals ½.

4. As t increases without bound, the graph approaches, but never equals, zero. As t decreases without bound the graph approaches, but never equals, zero.

4. As t increases without bound, the graph approaches, but never equals, zero. As t decreases without bound the graph approaches, but never equals, zero. 5. The area in the tails of the t distribution is a little greater than the area in the tails of the standard normal distribution. This result is because we are using s as an estimate of which introduces more variability to the t statistic.

Step 1: A claim is made regarding the population mean Step 1: A claim is made regarding the population mean. The claim is used to determine the null and alternative hypotheses. Again, the hypothesis can be structured in one of three ways:

Step 3: Compute the test statistic which follows Student’s t-distribution with n – 1 degrees of freedom.

Step 4: Compare the critical value with the test statistic:

Step 5 : State the conclusion.