9.6 #12 - Hypothesis Testing for Means

Hypothesis testing is a statistical method used to make decisions about the value of a population parameter based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (Ha), then using sample data to determine whether to reject H0.

The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing.

The alternative hypothesis (Ha) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

A z-test should be used when the population standard deviation is known and the sample size is large (typically n > 30).

A t-test should be used when the population standard deviation is unknown and/or the sample size is small (typically n ≤ 30).

The significance level (α) is the probability of rejecting the null hypothesis when it is actually true. Common values are 0.05, 0.01, and 0.10.

A p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the assumption that the null hypothesis is true.

Rejecting the null hypothesis means that there is sufficient evidence to support the alternative hypothesis.

Failing to reject the null hypothesis means that there is not enough evidence to support the alternative hypothesis.

A one-tailed test is a hypothesis test that evaluates the direction of the effect, testing whether a parameter is greater than or less than a certain value.