Do one of the following, as appropriate: (a) Find the critical value $\mathrm { z } _ { \alpha / 2 }$ , (b) find the critical value $t _ { \alpha / 2 }$ , (c) state that
neither the normal nor the t distribution applies.
-$91 \% ; \mathrm { n } = 45 ; \sigma$ is known; population appears to be very skewed.
A) $\mathrm { t } _ { \alpha / 2 } = 1.34$
B) $\mathrm { z } _ { \alpha / 2 } = 1.75$
C) $\mathrm { z } _ { \alpha / 2 } = 1.70$
D) $t _ { \alpha / 2 } = 1.645$

Question

Quizplus · Accepted Answer

Since the population appears to be very skewed, we cannot assume that the sample mean follows a normal distribution. Therefore, we cannot use the normal distribution to find the critical value. Instead, we need to use the z-distribution, which requires a large sample size (n > 30) and an assumption of normality. Since we do not have the latter assumption, we must use the t-distribution. However, since the population standard deviation is known, we can use the formula for the standard error of the mean (SE = σ/√n) to find the t-statistic. Therefore, neither option A nor option D is appropriate. The correct critical value for a 91% confidence interval with 45 degrees of freedom is 1.70, as found in a t-distribution table or using software.

Do One of the Following, as Appropriate: (A) Find the Critical