HYPOTHESIS TESTING FOR POPULATION PROPORTION

The video introduces the topic of hypothesis testing for population proportion, outlining the objectives: to distinguish and perform hypothesis testing for population proportions.

A problem is presented: determining if more than 50% of faculty approve a candidate for academic vice president. The first step involves formulating the null and alternative hypotheses. The alternative hypothesis states that the proportion is greater than 50% (0.5), while the null hypothesis states it's equal to 50%.

The second step is identifying the level of significance, which is given as 0.05. The third step involves choosing the appropriate test statistic, which for this problem, is a one-tailed test statistic.

Using the Z-table for a one-tailed test with a 0.05 significance level, the critical region is determined to be 1.645.

The fourth step is computing the Z-value using the formula for population proportion. The video walks through calculating 'p-hat' (sample proportion) and substituting values into the Z-formula.

The calculation of the Z-score is performed. After substituting the values and using a calculator, the computed Z-value is approximately -0.9136.

The final step involves deciding whether to accept or reject the null hypothesis by comparing the computed Z-value to the critical region. Since -0.9136 is not greater than 1.645, the statement is false, leading to the acceptance of the null hypothesis.

Based on the acceptance of the null hypothesis, it is concluded that there isn't sufficient evidence to state that more than 50% of the faculty approve the candidate.