Question

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.

10.58	9.28	11.9	6.6	12.52	14.63	15.66
10.22	14.6	16.28	17.7	19.28	18.08	12.95
16.9	17.45	15.74	14.9	19.01	18.09	15
18.52	16.15	26.95	22.42	22.86	21.08	23.55
19.15	23.8	19.36	23.85	27.9	27.15	27.24
27.09	24.78	37.96	26.61	39.11	29.56	41.75

(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:

H_a:

(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.

- 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.

- 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. (Enter != for ≠ as needed.)

H₀:

H_a:

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.

- 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.

- 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.

Answer 1

Given that,
population mean(u)=21.62
sample mean, x =20.338
standard deviation, s =7.705
number (n)=42
null, Ho: μ=21.62
alternate, H1: μ!=21.62
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.02
since our test is two-tailed
reject Ho, if to < -2.02 OR if to > 2.02
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =20.338-21.62/(7.705/sqrt(42))
to =-1.0783
| to | =1.0783
critical value
the value of |t α| with n-1 = 41 d.f is 2.02
we got |to| =1.0783 & | t α | =2.02
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != -1.0783 ) = 0.2872
hence value of p0.05 < 0.2872,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: μ=21.62
alternate, H1: μ!=21.62
b.
test statistic: -1.0783
critical value: -2.02 , 2.02
decision: do not reject Ho
c.
p-value: 0.2872
we do not have enough evidence to support the claim that 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