The state insurance commissioner believes that the mean automobile insurance claim filed in her state exceeds $1,700.To test this claim,the agency has selected a random sample of 20 claims and found a sample mean equal to $1,733 and a sample standard deviation equal to $400.They plan to conduct the test using a 0.05 significance level.Given this,the appropriate null and alternative hypotheses are
H₀ : ≤ $1,700
H_A : > $1,700

Question

The state insurance commissioner believes that the mean automobile insurance claim filed in her state exceeds $1,700.To test this claim,the agency has selected a random sample of 20 claims and found a sample mean equal to $1,733 and a sample standard deviation equal to $400.They plan to conduct the test using a 0.05 significance level.Given this,the appropriate null and alternative hypotheses are
H₀ :

≤ $1,700
H_A :

> $1,700

Quizplus · Accepted Answer

The appropriate null and alternative hypotheses for a one-tailed test with a significance level of 0.05 are:
- Null hypothesis (H0): the mean automobile insurance claim is less than or equal to $1,700
- Alternative hypothesis (Ha): the mean automobile insurance claim is greater than $1,700
Therefore, the correct null and alternative hypotheses are:
H0: μ ≤ $1,700
Ha: μ > $1,700
Based on this, the answer is B, as the null and alternative hypotheses presented in the question are reversed.

The State Insurance Commissioner Believes That the Mean Automobile Insurance