Question

A park ranger claims that the average number of acres in his State Park is less than 2000 acres.

A random sample of five parks is selected and the number of acres is shown below:
959, 1187, 493, 6249, 541
Assume the variable must be normally distributed, at
`\alpha =0.01` is there enough evidence to support the claim? To draw your conclusion, state the hypotheses and identify the claim, find the critical value(s), label the acceptance and rejection region, calculate the test value and summarize the results.

Answer 1

ypotheses:

H0: μ = 2000

H1: μ < 2000

Claim: The average number of acres in the State Park is less than 2000.

Critical Value (s): -1.645 (z-score)

Acceptance Region: z < -1.645

Rejection Region: z ≥ -1.645

Test Value: z = -3.537

Conclusion: Since -3.537 is less than -1.645, we reject the null hypothesis and accept the alternate view. There is enough evidence to support the claim that the average number of acres in the State Park is less than 2000.

Explanation: