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 63 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 121 kWh. At α=0.05​, can you support the​ claim? Complete parts​ (a) through​ (e). ​(a) Identify H0 and Ha. Choose the correct answer below.     A. H0​: μ=900 Ha​: μ≠900 ​(claim)   B. H0​: μ≤880 Ha​: μ>880 ​(claim)   C. H0​: μ≤900 Ha​: μ>900 ​(claim)   D. H0​: μ>880 ​(claim) Ha​: μ≤880   E. H0​: μ>900 ​(claim) Ha​: μ≤900   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 value is nothing.   B. The critical values are ±nothing. Identify the rejection​ region(s). Select the correct choice below.     A. The rejection regions are z<−1.64 and z>1.64.   B. The rejection region is z<1.64.   C. The rejection region is z>1.64. ​(c) Find the standardized test statistic. Use technology.   The standardized test statistic is z=nothing. ​(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 5​% significance​ level, there ▼   isis is notis not enough evidence to ▼   support reject the claim that the mean monthly residential electricity consumption in a certain region ▼   is less than is greater than is different from nothing kWh.   Click to select your answer(s).

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...