The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000. If the level of significance is 0.10, what is the critical value?
A) 1.65
B) 1.28
C) $\pm$1.28
D) $\pm$1.65

Question

Quizplus · Accepted Answer

Since the level of significance is 0.10, we need to find the critical value for a two-tailed test at the 0.05 level (half of 0.10). Using a standard normal distribution table or calculator, the critical z-value for a two-tailed test at the 0.05 level is approximately 1.65. However, we need to adjust for the standard deviation of the sample mean, which is given by dividing the standard deviation by the square root of the sample size. In this case, since we don't have a sample size, we assume it's large enough to use the population standard deviation of $2,000. Thus, the critical value is:
$20,000 ± (1.65)($2,000) = $20,000 ± $3,300 = $16,700 to $23,300.
Therefore, the best choice is D, which gives the correct critical value with the correct adjustment for the standard deviation of the sample mean.

The Mean Gross Annual Incomes of Certified Welders Are Normally ±\pm±

The Mean Gross Annual Incomes of Certified Welders Are Normally $\pm$