Question

the annual salaries (in dollars) of 14 randomly chosen fire fighters are listed. at α = 0.05, is there enough evidence t support the claim that the standard deviation of the annual salaries is different from $5350? assume the population i normally distributed. complete parts (a) through (e) below. 50,762 40,962 52,386 46,539 41,734 40,173 51,138 52,013 43,827 34,908 35,096 28,222 32,693 37,832 click the icon to view the chi - square distribution table. (a) write the claim mathematically and identify h₀ and hₐ. a. h₀: σ < 5350 (claim); hₐ: σ ≥ 5350 b. h₀: σ ≤ 5350 (claim); hₐ: σ > 5350 c. h₀: σ ≥ 5350; hₐ: σ < 5350 (claim) d. h₀: σ = 5350; hₐ: σ ≠ 5350 (claim)

Explanation:

The claim is that the standard deviation (\(\sigma\)) of annual salaries is different from 5350. In hypothesis testing, the null hypothesis (\(H_0\)) typically contains a statement of equality (or no difference), and the alternative hypothesis (\(H_a\)) contains the claim (if the claim is a difference). Here, the claim is "different from", so \(H_a\) should be \(\sigma
eq 5350\) (this is the claim), and \(H_0\) is the complement with equality, so \(H_0: \sigma = 5350\). Options A, B, and C have claims with inequality directions (less than, less than or equal, etc.) which do not match the "different from" claim.

Answer:

D. \( H_0: \sigma = 5350 \); \( H_a: \sigma
eq 5350 \) (Claim)