Question

find the critical value for a left - tailed test with $\alpha=0.05$ and $n = 48$.
a. $-2.33$
b. $-1.96$
c. $-2.575$
d. $-1.645$

Explanation:

Step1: Determine the distribution

Since \(n = 48\) (\(n\geq30\)), we can use the standard normal distribution (\(Z -\)distribution) for hypothesis - testing.

Step2: Recall the property of left - tailed test

For a left - tailed test with significance level \(\alpha\), the critical value \(z\) satisfies \(P(Z\lt z)=\alpha\).
Given \(\alpha = 0.05\).

Step3: Look up the value in the standard normal table

Looking up the value in the standard normal table (or using a calculator with a normal - distribution function, e.g., \(z=\text{invNorm}(0.05)\) in TI - 84), we find that the \(z\) - value corresponding to an area of \(0.05\) in the left - tail of the standard normal distribution.

Answer:

D. \(-1.645\)