Which type of hypothesis test is used when the alternative hypothesis is expressed as not equal to a value?

Which type of hypothesis test is used when the alternative hypothesis is expressed as not equal to a value?

• A. One-tail hypothesis test
• B. Two-tail hypothesis test
• C. Null hypothesis test
• D. Paired t-test

Answer: (B)

When the alternative hypothesis states not equal to a value, the test is two-tailed. This means the null hypothesis asserts equality to that value, while the alternative covers departures in both directions (either higher or lower). Because evidence could show a difference on either side, the rejection region sits in both tails of the sampling distribution. For a typical significance level, you allocate half to each tail, so you reject if the test statistic is far in the positive direction or far in the negative direction. In practice, you’d compare the observed statistic to the critical values in both tails, or compute a two-tailed p-value that reflects extremity in either direction. A one-tailed test would be used only if the alternative specified a single direction (greater than or less than). A null hypothesis test is a general term for testing any H0, and a paired t-test applies when comparing two related samples, not when deciding between a two-sided versus one-sided alternative.

When the alternative hypothesis states not equal to a value, the test is two-tailed. This means the null hypothesis asserts equality to that value, while the alternative covers departures in both directions (either higher or lower).

Because evidence could show a difference on either side, the rejection region sits in both tails of the sampling distribution. For a typical significance level, you allocate half to each tail, so you reject if the test statistic is far in the positive direction or far in the negative direction. In practice, you’d compare the observed statistic to the critical values in both tails, or compute a two-tailed p-value that reflects extremity in either direction.

A one-tailed test would be used only if the alternative specified a single direction (greater than or less than). A null hypothesis test is a general term for testing any H0, and a paired t-test applies when comparing two related samples, not when deciding between a two-sided versus one-sided alternative.