Question

you can calculate the p-value for a chi-square test using technology. after calculating the standardized test statistic, use the cumulative distribution function (cdf) to calculate the area under the curve. use the p-value method to test the claim.
a hospital spokesperson claims that the standard deviation of the waiting times experienced by patients in its minor emergency department is no more than 0.5 minutes. a random sample of 23 waiting times has a standard deviation of 0.7 minutes. at α = 0.05, is there enough evidence to reject the spokesperson’s claim?
identify the null and alternative hypotheses.
a. h₀: σ < 0.5
hₐ: σ ≥ 0.5
b. h₀: σ ≤ 0.5
hₐ: σ > 0.5
c. h₀: σ ≥ 0.5
hₐ: σ < 0.5
d. h₀: σ > 0.5
hₐ: σ ≤ 0.5

Explanation:

1. The null hypothesis (\( H_0 \)) always contains the equality or the claim being tested (in this case, the spokesperson's claim that the standard deviation is no more than 0.5 minutes, i.e., \( \sigma \leq 0.5 \)).
2. The alternative hypothesis (\( H_a \)) is the opposite of the null hypothesis and is what we might believe if we reject the null. Since we are testing if there's evidence the standard deviation is more than 0.5, \( H_a: \sigma > 0.5 \).

Answer:

B. \( H_0: \sigma \leq 0.5 \)
\( H_a: \sigma > 0.5 \)