An energy company changed its billing method in a small town claiming that the change would decrease the mean energy bill for customers. Under the old plan the mean monthly cost in the town was $225. To test the claim a sample of 47 energy bills were checked and the mean bill was $211 with a standard deviation of $89. Show all the steps and work to test the company’s claim at the 5% significance level.
An energy company changed its billing method in a small town claiming that the change would decrease the mean energy bill for customers. Under the old plan the mean monthly cost in the town was $225. To test the claim a sample of 47 energy bills were checked and the mean bill was $211 with a standard deviation of $89. Show all the steps and work to test the company’s claim at the 5% significance level.
An energy company changed its billing method in a small town claiming that the change would decrease the mean energy bill for customers. Under the old plan the mean monthly cost in the town was $225. To test the claim a sample of 47 energy bills were checked and the mean bill was $211 with a standard deviation of $89. Show all the steps and work to test the company’s claim at the 5% significance level.
An energy company changed its billing method in a small town claiming that the change would decrease the mean energy bill for customers. Under the old plan the mean monthly cost in the town was $225. To test the claim a sample of 47 energy bills were checked and the mean bill was $211 with a standard deviation of $89. Show all the steps and work to test the company’s claim at the 5% significance level.
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 + ...
Expert Solution
Step 1
Hypothesis:
The null and alternative hypotheses are below:
The test statistic is obtained as below:
Thus, the test statistic is -1.0784
Step 2
Degrees of freedom:
P-value:
The test statistic is |–1.0784|=1.0784. The P-value is obtained Excel function “=TDIST(x, degrees of freedom, tails)”.
Output obtained using Excel is as follows:
From the output, the p-value is 0.8568(=(1-0.1432)).
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