Question

find the critical value for a left - tailed test with \\( \alpha = 0.025 \\) and \\( n = 50 \\).

a. \\( - 2.575 \\)
b. \\( - 1.645 \\)
c. \\( - 1.96 \\)
d. \\( - 2.33 \\)

Explanation:

Step1: Determine the distribution

Since \(n = 50\) (\(n\geq30\)), we can use the standard normal distribution (\(Z -\)distribution) for finding the critical value.

Step2: Recall the property of left - tailed test

For a left - tailed test with significance level \(\alpha\), the critical value \(z\) satisfies \(P(Z<z)=\alpha\).
Given \(\alpha = 0.025\).

Step3: Look up the \(z -\)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., for a TI - 84: invNorm(0.025,0,1)), we know that the \(z -\)value corresponding to a left - tailed area of \(\alpha=0.025\) is \(z=- 1.96\).

Answer:

C. \(-1.96\)