A company claims that the mean monthly residential electricity consumption in a certain region is more than 880 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 64 residential customers has a mean monthly consumption of 910 kWh. Assume the population standard deviation is 124 kWh. At α = 0.01, can you support the claim? Complete parts (a) through (e).
(a) Identify H₀ and Hₐ. Choose the correct answer below.
A. H₀: μ > 910 (claim)
Hₐ: μ ≤ 910
B. H₀: μ = 910
Hₐ: μ ≠ 910 (claim)
C. H₀: μ ≤ 910
Hₐ: μ > 910 (claim)
D. H₀: μ ≤ 880
Hₐ: μ > 880 (claim)
E. H₀: μ > 880 (claim)
Hₐ: μ ≤ 880
F. H₀: μ = 880 (claim)
Hₐ: μ ≠ 880
(b) Find the critical value(s) and identify the rejection region(s). Select the correct choice below and fill in the answer box within your choice. Use technology.
(Round to two decimal places as needed.)
A. The critical values are ± [ ].
B. The critical value is 2.33.
Identify the rejection region(s). Select the correct choice below.
A. The rejection region is z > 2.33.
B. The rejection region is z < 2.33.
C. The rejection regions are z < − 2.33 and z > 2.33.
(c) Find the standardized test statistic. Use technology.
The standardized test statistic is z = [ ].
(Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
A. Reject H₀ because the standardized test statistic is in the rejection region.
B. Reject H₀ because the standardized test statistic is not in the rejection region.
C. Fail to reject H₀ because the standardized test statistic is not in the rejection region.
D. Fail to reject H₀ because the standardized test statistic is in the rejection region.
(e) Interpret the decision in the context of the original claim.
At the 1% significance level, there [ ] enough evidence to [ ] the claim that the mean monthly residential electricity consumption in a certain region [ ] kWh.
