I want to test H0: p = .12 vs. Ha: p ≠ .12 using a test of hypothesis. This test would be called a(n) ____________ test.

A) two-tailed
B) right-tailed (this one?)
C) left-tailed

Answer. A

To test the hypothesis H0: p = .12 against Ha: p ≠ .12, we need to use a two-tailed test.

A two-tailed test is used when we are interested in determining whether a population parameter is significantly different from a specific value, but we do not have a specific direction in mind. In this case, the alternative hypothesis Ha: p ≠ .12 suggests that the true population proportion may be either higher or lower than .12.

To conduct the two-tailed test, you would typically follow these steps:
1. Set up the null and alternative hypotheses:
- Null Hypothesis (H0): p = .12
- Alternative Hypothesis (Ha): p ≠ .12

2. Collect a sample of data and calculate the sample proportion (p-hat) based on the collected data.

3. Determine the significance level (α) for the test. The significance level, often denoted as α, represents the probability of rejecting the null hypothesis when it is actually true. Common choices for α are 0.05 (5%) or 0.01 (1%).

4. Calculate the test statistic. For proportions, the test statistic is typically the z-score, which measures how many standard deviations the sample proportion is away from the hypothesized proportion under the null hypothesis. The formula for the z-score is:
z = (p-hat - p) / sqrt(p * (1-p) / n)
where p-hat is the sample proportion, p is the hypothesized proportion under the null hypothesis, and n is the sample size.

5. Determine the critical value(s). Since this is a two-tailed test, you would need to find critical values in both tails of the z-distribution. The critical values depend on the significance level (α) and can be obtained from a z-table or calculated using statistical software.

6. Compare the test statistic to the critical value(s) and make a decision. If the absolute value of the test statistic is greater than the critical value(s), we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis. If the absolute value of the test statistic is not greater than the critical value(s), we fail to reject the null hypothesis and do not have sufficient evidence to support the alternative hypothesis.

In summary, to test H0: p = .12 vs. Ha: p ≠ .12, we would use a two-tailed test.