i. If the null hypothesis is $\mu$ $\ge$ 200 and the alternate hypothesis states that $\mu$ is less than 200, then, a two-tail test is being conducted. ii. For a one-tailed test of hypothesis, the area of rejection is only in one tail of the curve.
iii. As the sample size increases, the curve of the t-distribution approaches the standard normal distribution
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

- Statement (i) is incorrect because when the alternate hypothesis specifies a direction (e.g., "less than 200"), a one-tailed test is conducted, not a two-tailed test.- Statement (ii) is correct because in a one-tailed test, the area of rejection is indeed only in one tail of the distribution curve, either the left or the right depending on the direction of the hypothesis.- Statement (iii) is correct because as the sample size increases, the t-distribution becomes more similar to the standard normal distribution due to the central limit theorem.

I If the Null Hypothesis Is μ\muμ ≥\ge≥ 200 and the Alternate Hypothesis States That

I If the Null Hypothesis Is $\mu$ $\ge$ 200 and the Alternate Hypothesis States That