Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
$H_0:$ $p=0.4$
$H_a:$ $p\ne 0.4$

• A. Left-tailed
• B. Right-tailed
• C. Two-tailed

Answer: (C)

Verified step by step guidance

1. Identify the null hypothesis (H0) and the alternative hypothesis (Ha). In this problem, H0: p = 0.4 and Ha: p ≠ 0.4.
2. Understand the meaning of the null hypothesis (H0). It states that the population proportion p is equal to 0.4.
3. Understand the meaning of the alternative hypothesis (Ha). It states that the population proportion p is not equal to 0.4.
4. Determine the type of test based on the alternative hypothesis. If Ha uses '≠', it indicates a two-tailed test because we are interested in deviations on both sides of the null hypothesis value.
5. Conclude that the hypothesis test is two-tailed because the alternative hypothesis Ha: p ≠ 0.4 suggests that we are testing for any significant difference from 0.4, either greater or less.