Question

a hospital spokesperson claims that the standard deviation of the waiting times experienced by patients in its minor emergency department is no more than 0.7 minutes. a random sample of 28 waiting times has a standard deviation of 0.8 minutes. at α = 0.10, is there enough evidence to reject the spokespersons claim? assume the population is normally distributed. complete parts (a) through (e) below. click the icon to view the chi - square distribution table. (a) write the claim mathematically and identify h₀ and hₐ. a. h₀:σ ≤ 0.7 (claim); hₐ:σ > 0.7 b. h₀:σ ≥ 0.7; hₐ:σ < 0.7 (claim) c. h₀:σ = 0.7; hₐ:σ ≠ 0.7 (claim) d. h₀:σ < 0.7 (claim); hₐ ≥ 0.7

Explanation:

The hospital spokesperson claims the standard deviation ($\sigma$) of waiting times is no more than 0.7 minutes, so the claim is $\sigma\leq0.7$. The null hypothesis ($H_0$) contains the claim, and the alternative hypothesis ($H_a$) is the opposite (here, $\sigma > 0.7$) to test if there's evidence to reject the claim. Option A matches this: $H_0$ has the claim $\sigma\leq0.7$ and $H_a$ is $\sigma > 0.7$.

Answer:

A. $H_0:\sigma\leq0.7$ (Claim); $H_a:\sigma > 0.7$