Question 5 of 12
We're testing the hypothesis that the average boy walks at 18 months of age ( H_{0}*mu = 18 . We assume that the ages at which boys walk is approximately normally distributed with a standard deviation of 2.5 months. A random sample of 25 boys has a mean of 19.2 months. Which of the following statements are correct?
1. This finding is significant for a two-tailed test at .05.
II. This finding is significant for a two-tailed test at .01.
III. This finding is significant for a one-tailed test at .01.
A. I only
B. II only
C. III only
D. II and III only
E. I and III only
To determine which statements are correct, we need to calculate the z-value and compare it to the critical z-value for each significance level.
First, we calculate the z-value using the formula:
z = (x̄ - μ) / (σ / sqrt(n))
z = (19.2 - 18) / (2.5 / sqrt(25))
z = 1.2 / (2.5 / 5)
z = 1.2 / 0.5
z = 2.4
I. For a two-tailed test at .05 significance level, the critical z-value is approximately ±1.96. Since the calculated z-value of 2.4 is greater than 1.96, we reject the null hypothesis and the finding is significant for a two-tailed test at .05. Therefore, statement I is correct.
II. For a two-tailed test at .01 significance level, the critical z-value is approximately ±2.58 (since we are decreasing the level of significance, the critical value increases). The calculated z-value of 2.4 is less than 2.58, so we fail to reject the null hypothesis. Therefore, statement II is incorrect.
III. For a one-tailed test at .01 significance level, the critical z-value is approximately 2.33 (since the test is one-tailed, the critical value is a single value). Since the calculated z-value of 2.4 is greater than 2.33, we reject the null hypothesis. Therefore, statement III is correct.
Therefore, the correct statements are:
I. This finding is significant for a two-tailed test at .05
III. This finding is significant for a one-tailed test at .01
The answer is E. I and III only.