On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The data shown below ($) contains the rate per 5 CCF of residential water for 42 randomly selected U.S. cities.
10.48 | 9.18 | 11.8 | 6.5 | 12.42 | 14.53 | 15.56 |
10.12 | 14.5 | 16.18 | 17.6 | 19.18 | 17.98 | 12.85 |
16.8 | 17.35 | 15.64 | 14.8 | 18.91 | 17.99 | 14.9 |
18.42 | 16.05 | 26.85 | 22.32 | 22.76 | 20.98 | 23.45 |
19.05 | 23.7 | 19.26 | 23.75 | 27.8 | 27.05 | 27.14 |
26.99 | 24.68 | 37.86 | 26.51 | 39.01 | 29.46 | 41.65 |
(a)
Formulate hypotheses that can be used to determine whether the population mean rate per 5 CCF of residential water charged by U.S. public utilities differs from the $21.62 rate charged by Tulsa. (Enter != for ≠ as needed.)
H0:
μ=21.62
Ha:
μ!=21.62
(b)
What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.)
What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.)
(c)
At α = 0.05, can your null hypothesis be rejected? What is your conclusion?
Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa. Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.
(d)
Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:
Ha:
Find the value of the test statistic. (Round your answer to three decimal places.)
State the critical values for the rejection rule. Use
α = 0.05.
(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic≤test statistic≥
State your conclusion.
Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa. Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.
a)
H0: μ=21.62
Ha: μ!=21.62
b)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (20.2383 - 21.62)/(7.7991/sqrt(42))
t = -1.148
P-value Approach
P-value = 0.2576
c)
Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa
d)
H0: μ=21.62
Ha: μ!=21.62
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (20.2383 - 21.62)/(7.7991/sqrt(42))
t = -1.148
This is two tailed test, for α = 0.05 and df = 41
Critical value of t are -2.020 and 2.020.
Hence reject H0 if test statistic <= -2.020
test statistic > 2.020
Do not reject H0. The mean rate per 5 CCF of residential water
throughout the United States does not differ significantly from the
rate per 5 CCF of residential water in Tulsa
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