1. More Hypothesis Testing
Chapter 9, part D
More Hypothesis Testing

2. V. Tests about : Small sample case
If you have a small (n<30) sample, it’s appropriate to use the t-distribution for hypothesis testing.
Your test statistic,
has a t-distribution with (n-1) degrees of freedom.

3. A. One-Tailed Test
Historically the population of Hanover students has a cumulative G.P.A. of no more than Suppose you want to test the hypothesis that (due to smarter students) the mean GPA is higher.
Ho:   2.77
Ha:  > 2.77

4. The Test
In a sample of 25 students, you calculate a mean GPA of and a standard deviation of
Test the hypothesis at the 95% confidence.
Your critical t.05 with 24 degrees of freedom is
The test statistic: =.8246
You can’t reject Ho and must conclude that the GPA has not increased.

5. B. Two-Tailed Test
A golf ball producer tests driving distance of a new golf ball. Due to PGA specifications, the distance needs to average 280 yards.
Ho:  = 280 yds.
Ha:   280 yds.

6. The Test
You sample n=10 golf balls, calculate a sample mean of yards and a standard deviation of
With 9 degrees of freedom, the critical t.025=±2.262
Your test statistic is .514, so you cannot reject Ho.
Your conclusion is that the golf balls are o.k.
Can you do this?

7. VI. Tests about a population proportion
The techniques are virtually identical to those testing a population mean.
“p” is the population proportion, and p0 is the hypothesized value of the population proportion.
One and two-tailed tests are structured in the same way as before.

8. A. Testing a proportion hypothesis
The main difference when dealing with a proportion problem is in the calculation of the standard error. Recall from chapter 7:
We also have to test to see if we can safely apply the Central Limit Theorem.
If np>=5 and n(1-p)>=5, our sample is “large enough”.

9. B. An example
A restaurant believes that 30% of their customers do not drink water with their meal. In a recent sample of 480 customers, 128 did not drink their water. Use this sample to test their belief at a 95% confidence level.

10. Ho:  = .30.
Ha:   .30
p-bar = 128/480 =.2667.
= .0209
The critical value is  1.96 and the test statistic is Z = so we fail to reject the null.