Statistical Testing Notes

Sample Size and Test Selection

• The sample size is important in statistical testing.
• If the sample size is less than 30, the t-test is preferred over the z-test.

Understanding Test Statistics

• The test statistic in this case was calculated to be -1.383.
• When comparing the test statistic to a significance level (alpha), it's essential to check where it lies in relation to the critical value.

P Value and Hypothesis Testing

• The P value in this scenario is less than the significance level of 10%.
• When using the P value method, if the P value is less than the significance level, we have enough evidence to reject the null hypothesis.
• If using the proportion test, remember the following:
  • The required calculations involve the sample proportion, denoted as $\hat{p}$, computed as ( \hat{p} = \frac{x}{n} ) where:
  • x = number of successes
  • n = total sample size
  • The complement of the proportion can be referred to as $q$, which is evaluated as $q = 1 - p$.

Following Steps in Hypothesis Testing

• To conduct a hypothesis test, one typically follows five steps:
  1. State the null and alternative hypothesis.
  2. Select a significance level (alpha).
  3. Calculate the test statistic.
  4. Determine the P value.
  5. Make a decision about the null hypothesis.

Example Analysis

• The conclusion drawn was that the test statistic fell into the non-critical region, which means:
  • The null hypothesis could not be rejected.
  • The analysis led to a conclusion based on a test statistic of 1.19, and since this was a two-tailed test, more careful consideration was needed around this value.