A company claims that the mean monthly residential electricity consumption in a certain region is more than 860kiloWatt−hours(kWh). You want to test this claim. You find that a random sample of 65 residential customers has a mean monthly consumption of 890kWh. Assume the population standard deviation is 128kWh. At α=0.01, can you support the claim? Complete parts (a) through ( 0 ).(a) Identify H0 and Ha. Choose the correct answer below.A. H0:μH8:μ≤860gt;860 (claim) B. H0:μHa:μ≤890gt;890 (claim) c. H0:μ≤890H2:μgt;890 (claim) D. H0:μ=860 (claim) Ha:μ=860E. H0:μ=890H8:μ=890 (daim) F. H0:μ≤860Ha:μgt;860 (claim)
Q. A company claims that the mean monthly residential electricity consumption in a certain region is more than 860kiloWatt−hours(kWh). You want to test this claim. You find that a random sample of 65 residential customers has a mean monthly consumption of 890kWh. Assume the population standard deviation is 128kWh. At α=0.01, can you support the claim? Complete parts (a) through ( 0 ).(a) Identify H0 and Ha. Choose the correct answer below.A. H0:μ>860 (claim) H8:μ≤860B. H0:μ>890 (claim) Ha:μ≤890c. H0:μ≤890H2:μ>890 (claim) D. H0:μ=860 (claim) Ha:μ=860E. H0:μ=890H8:μ=890 (daim) F. H0:μ≤860Ha:μ>860 (claim)
Define Hypotheses: The first step in hypothesis testing is to define the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis typically represents the status quo or a statement of no effect, while the alternative hypothesis represents what we are trying to show or the claim being tested.
Company Claim: In this case, the company claims that the mean monthly residential electricity consumption is more than 860kWh. This is the claim we are trying to support, so it should be reflected in the alternative hypothesis (Ha). The null hypothesis should be the opposite of the claim or the statement that there is no effect.
Correct Hypotheses: The correct null and alternative hypotheses are therefore:H₀: μ≤860 (the mean is less than or equal to860 kWh, which is the opposite of the claim)Hₐ: \mu > 860 (the mean is greater than 860 kWh, which is the claim)
Correct Answer: Looking at the options provided, the correct answer is:F. \left\{\begin{array}{l}H_{0}:\mu \leq 860\H_{a}:\mu > 860\ \text{(claim)}\end{array}\right.This is because the null hypothesis is the opposite of the claim (that the mean is more than 860 kWh), and the alternative hypothesis is the claim itself.
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