Question

an online retailer employs 1,300 employees. one of their competitors would like to test the hypothesis that the average age of these 1,300 employees is less than 36 years old. a random sample of 22 employees was found to have an average age of 33.9 years. the standard deviation for this sample was 4.1 years. the competitor would like to set \\( \alpha = 0.025 \\). what is the correct hypothesis statement for this hypothesis test?

a. \\( h _ { 0 } : \mu \leq 36 ; h _ { 1 } : \mu > 36 \\)
b. \\( h _ { 0 } : \mu \geq 36 ; h _ { 1 } : \mu < 36 \\)
c. \\( h _ { 0 } : \mu = 36 ; h _ { 1 } : \mu \
eq 36 \\)
d. \\( h _ { 0 } : \mu = 33.9 ; h _ { 1 } : \mu \
eq 33.9 \\)

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) represents the status - quo or the claim we assume to be true initially. The alternative hypothesis \(H_1\) is what we are trying to find evidence for. Here, the claim is that the average age \(\mu\) is less than 36. So the null hypothesis should be the opposite of the claim (a statement of equality or a "greater - than - or - equal - to" relationship when the alternative is "less - than") and the alternative hypothesis is \(\mu<36\).

Answer:

B. \(H_0:\mu\geq36;H_1:\mu < 36\)