Final answer:
Hypothesis testing involves setting up a null hypothesis (H-o) and an alternative hypothesis (Ha) to test against each other using sample data. A significance level (alpha, α) is chosen to determine the cutoff for rejecting H-o based on the p-value. If the p-value is below α, the null hypothesis is rejected indicating significant evidence against it.
Step-by-step explanation:
Understanding Hypothesis Testing
Hypothesis testing is a statistical method that is used in making decisions using experimental data. A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. When we talk about hypothesis testing, we often refer to the null hypothesis (H-o) and the alternative hypothesis (Ha).
Setting Up Hypotheses
For a study determining if the majority of women aged 22 to 35 who work full-time would be willing to give up some personal time for more money, the correct null hypothesis (H-o) would typically be set up to reflect no change or difference from what is already established or expected. Therefore, we could set it as H-o: p ≤ 0.50, which states that the proportion of women willing to give up personal time for more money is half or less. The alternative hypothesis (Ha) would then be the statement that reflects the researcher's belief, which is that a majority of women would be willing to give up some personal time for more money; this could be set as Ha: p > 0.50.
If we were comparing two independent population proportions, as in the case of the number of households with cable service in Community A and Community B, the null hypothesis would be H-o: p1 = p2, which states that the proportions are the same, while the alternative hypothesis would be Ha: p1 ≠ p2, indicating that there is a difference between the two proportions.
When conducting hypothesis testing, we also need to decide on a significance level (alpha, α), which is the probability of rejecting the null hypothesis when it is actually true. Common choices for α are 0.05 or 0.01.
P-value and Decision Making
The p-value helps us determine the significance of our results in relation to the chosen alpha level. If the p-value is less than or equal to α, we reject the null hypothesis; otherwise, we fail to reject it.
For instance, with a p-value of 0.0033 and α = 0.05, we would reject the null hypothesis, as the p-value is below the significance level. This leads to the conclusion that there is sufficient evidence to suggest a significant difference.