Question

which of the following is not true about the tails in a distribution?

choose the correct answer below

a. the inequality symbol in the alternative hypothesis points away from the critical region.
b. the critical region in a left - tailed test is in the extreme left tail
c. the symbol ≠ is often expressed in computer science as <>, and this is a great reminder that an alternative hypothesis with the symbol ≠ corresponds to a two tailed test
d. the tails in a distribution are the extreme critical regions bounded by critical values

Explanation:

• Option A:
• In hypothesis - testing, the inequality symbol in the alternative hypothesis points towards the critical region. For example, if \(H_a: \mu>\mu_0\) (right - tailed test), the critical region is in the right - tail.
• Option B:
• By the definition of a left - tailed test, the critical region is in the extreme left tail. If we have a significance level \(\alpha\), we find the \(z\) - score (or \(t\) - score etc.) such that \(P(Z < z_{\alpha})=\alpha\) for a standard normal distribution \(Z\).
• Option C:
• In computer science, \(

eq\) is often written as \(<>\). When the alternative hypothesis is \(H_a:\mu
eq\mu_0\), we have two critical regions (two - tailed test). One in the left tail \(P(Z < - z_{\alpha/2})\) and one in the right tail \(P(Z>z_{\alpha/2})\) where the total area of the two tails is \(\alpha\).

• Option D:
• The tails in a distribution (for hypothesis - testing) are the extreme regions. For a normal distribution \(N(\mu,\sigma^{2})\), if we are doing a hypothesis test at significance level \(\alpha\), the critical values (e.g., \(z_{\alpha/2}\) for a two - tailed \(z\) - test) bound the tails (critical regions). The area of the tails (critical regions) is \(\alpha\).

Answer:

A. The inequality symbol in the alternative hypothesis points away from the critical region.