In: Statistics and Probability
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.
10.68 | 9.38 | 12 | 6.7 | 12.62 | 14.73 | 15.76 |
10.32 | 14.7 | 16.38 | 17.8 | 19.38 | 18.18 | 13.05 |
17 | 17.55 | 15.84 | 15 | 19.11 | 18.19 | 15.1 |
18.62 | 16.25 | 27.05 | 22.52 | 22.96 | 21.18 | 23.65 |
19.25 | 23.9 | 19.46 | 23.95 | 28 | 27.25 | 27.34 |
27.19 | 24.88 | 38.06 | 26.71 | 39.21 | 29.66 | 41.85 |
(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:
Ha:
(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 differs 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 does not differ 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.
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 differs 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 does not differ significantly from the rate per 5 CCF of residential water in Tulsa.
a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 21.62
Alternative Hypothesis, Ha: μ ! 21.62
b)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (20.4383 - 21.62)/(7.7991/sqrt(42))
t = -0.982
P-value Approach
P-value = 0.3319
As P-value >= 0.05, fail to reject null hypothesis.
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)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 21.62
Alternative Hypothesis, Ha: μ ! 21.62
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (20.4383 - 21.62)/(7.7991/sqrt(42))
t = -0.982
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.