Question 1026628: The US Energy Information Association claims that the mean monthly residential electricity consumption in your town is more than 874 kilowatt hours. You want to test this claim. You find that a random sample of 64 residential customers have an average monthly electricity consumption of 905 kilowatt hours. Assume that population standard deviation is 125 kilowatt hours. At alpha=0.05, do you have enough evidence to support the associations claim?
a. show the null and alternative hypotheses, show which is the claim.
b. find the critical values and identify the rejection on a bell curve
c. find the test statistic z
d. decide whether to reject the null or fail to reject the null
e. interpret the decision in the context of the original claim
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a) Ho = monthly population mean of residential power consumption is equal to 874 kilowatts
H1 = monthly population mean of residential power consumption greater than 874 (claim)
:
b) We use a one-tailed test
significance level is 5% or 0.05
note that the standard deviation is the square root of the variance
we want to calculate the standard error of the population mean
standard error of the population mean = square root ( variance / sample size )
standard error of the population mean = 125 / 8 = 15.625
At a 5% significance level, the critical value for a one tailed test is found from the table of z-scores to be 1.645.
:
c) our test statistic z = (904 - 874) / 15.625 = 1.92
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d) since our test statistic falls within the critical region ( x > or = 1.645), we reject the null hypothesis
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e) The statistical evidence shows that either a rare event has occurred, or that the population mean of residential power consumption is in fact greater than 874 kilowatts.
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