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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 alpha=0.01, can you support the claim? Complete parts (a) through ( 0 ).
(a) Identify H_(0) and H_(a). Choose the correct answer below.
A. {:[H_(0):mu > 860" (claim) "],[H_(8):mu <= 860]:}
B. {:[H_(0):mu > 890" (claim) "],[H_(a):mu <= 890]:}
c. {:[H_(0):mu <= 890],[H_(2):mu > 890" (claim) "]:}
D. {:[H_(0):mu=860" (claim) "],[H_(a):mu!=860]:}
E. {:[H_(0):mu=890],[H_(8):mu!=890" (daim) "]:}
F. {:[H_(0):mu <= 860],[H_(a):mu > 860" (claim) "]:}

A company claims that the mean monthly residential electricity consumption in a certain region is more than 860kiloWatthours(kWh). 860 \mathrm{kiloWatt-hours} \mathrm{(kWh).} You want to test this claim. You find that a random sample of 6565 residential customers has a mean monthly consumption of 890kWh 890 \mathrm{kWh} . Assume the population standard deviation is 128kWh 128 \mathrm{kWh} . At α=0.01 \alpha=0.01 , can you support the claim? Complete parts (a) through ( 00 ).\newline(a) Identify H0 \mathrm{H}_{0} and Ha \mathrm{H}_{\mathrm{a}} . Choose the correct answer below.\newlineA. H0:μgt;860 (claim) H8:μ860 \begin{array}{l} H_{0}: \mu&gt;860 \text { (claim) } \\ H_{8}: \mu \leq 860 \end{array} \newlineB. H0:μgt;890 (claim) Ha:μ890 \begin{array}{l} H_{0}: \mu&gt;890 \text { (claim) } \\ H_{a}: \mu \leq 890 \end{array} \newlinec. H0:μ890H2:μgt;890 (claim)  \begin{array}{l} H_{0}: \mu \leq 890 \\ H_{2}: \mu&gt;890 \text { (claim) } \end{array} \newlineD. H0:μ=860 (claim) Ha:μ860 \begin{array}{l} H_{0}: \mu=860 \text { (claim) } \\ H_{a}: \mu \neq 860 \end{array} \newlineE. H0:μ=890H8:μ890 (daim)  \begin{array}{l} H_{0}: \mu=890 \\ H_{8}: \mu \neq 890 \text { (daim) } \end{array} \newlineF. H0:μ860Ha:μgt;860 (claim)  \begin{array}{l} H_{0}: \mu \leq 860 \\ H_{a}: \mu&gt;860 \text { (claim) } \end{array}

Full solution

Q. A company claims that the mean monthly residential electricity consumption in a certain region is more than 860kiloWatthours(kWh). 860 \mathrm{kiloWatt-hours} \mathrm{(kWh).} You want to test this claim. You find that a random sample of 6565 residential customers has a mean monthly consumption of 890kWh 890 \mathrm{kWh} . Assume the population standard deviation is 128kWh 128 \mathrm{kWh} . At α=0.01 \alpha=0.01 , can you support the claim? Complete parts (a) through ( 00 ).\newline(a) Identify H0 \mathrm{H}_{0} and Ha \mathrm{H}_{\mathrm{a}} . Choose the correct answer below.\newlineA. H0:μ>860 (claim) H8:μ860 \begin{array}{l} H_{0}: \mu>860 \text { (claim) } \\ H_{8}: \mu \leq 860 \end{array} \newlineB. H0:μ>890 (claim) Ha:μ890 \begin{array}{l} H_{0}: \mu>890 \text { (claim) } \\ H_{a}: \mu \leq 890 \end{array} \newlinec. H0:μ890H2:μ>890 (claim)  \begin{array}{l} H_{0}: \mu \leq 890 \\ H_{2}: \mu>890 \text { (claim) } \end{array} \newlineD. H0:μ=860 (claim) Ha:μ860 \begin{array}{l} H_{0}: \mu=860 \text { (claim) } \\ H_{a}: \mu \neq 860 \end{array} \newlineE. H0:μ=890H8:μ890 (daim)  \begin{array}{l} H_{0}: \mu=890 \\ H_{8}: \mu \neq 890 \text { (daim) } \end{array} \newlineF. H0:μ860Ha:μ>860 (claim)  \begin{array}{l} H_{0}: \mu \leq 860 \\ H_{a}: \mu>860 \text { (claim) } \end{array}
  1. Define Hypotheses: The first step in hypothesis testing is to define the null hypothesis (H0H_0) and the alternative hypothesis (HaH_a). 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.
  2. Company Claim: In this case, the company claims that the mean monthly residential electricity consumption is more than 860kWh860 \, \text{kWh}. This is the claim we are trying to support, so it should be reflected in the alternative hypothesis (HaH_a). The null hypothesis should be the opposite of the claim or the statement that there is no effect.
  3. Correct Hypotheses: The correct null and alternative hypotheses are therefore:\newlineH₀: μ860\mu \leq 860 (the mean is less than or equal to 860860 kWh, which is the opposite of the claim)\newlineHₐ: \mu > 860 (the mean is greater than 860860 kWh, which is the claim)
  4. Correct Answer: Looking at the options provided, the correct answer is:\newlineF. \left\{\begin{array}{l}H_{0}:\mu \leq 860\H_{a}:\mu > 860\ \text{(claim)}\end{array}\right.\newlineThis is because the null hypothesis is the opposite of the claim (that the mean is more than 860860 kWh), and the alternative hypothesis is the claim itself.

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