Question

During the winter of​ 2008-2009, the average utility bill for residents of a certain state was ​$184 per month. A random sample of 40 customers was selected during the winter of​ 2009-2010, and the average bill was found to be ​$174.91 with a sample standard deviation of ​$19.47

.Complete parts a and b below.

​a) Using alpha=0.05 ​,does this sample provide enough evidence to conclude that the average utility bill in this state was lower in the winter of​ 2009-2010 than it was in the winder of​ 2008-2009?

Determine the hypotheses.

A. Upper H 0 ​: mu less than or equals 184 and Upper H 1 ​: mu greater than 184

B.Upper H 0 ​: mu not equals 184 and Upper H 1 ​: mu equals 184

C. Upper H 0 ​: mu greater than or equals 184 and Upper H 1 ​: mu less than 184

D.Upper H 0 ​: mu =184 and Upper H 1 ​: mu not equals 184

Determine the critical​ value(s).

The critical​ value(s) is(are) .

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Determine the test​ statistic, t Subscript x overbar

.t Subscript x overbar =

​(Round to two decimal places as​ needed.)

What conclusion should be​ drawn?

A.Do not reject Upper H 0 . There is not sufficient evidence to conclude that the average utility bill in this state was lower in the winter of​ 2009-2010 than it was in the winter of​ 2008-2009.

B. Reject Upper H 0 . There is sufficient evidence to conclude that the average utility bill in this state was lower in the winter of​ 2009-2010 than it was in the winter of​ 2008-2009.

C. Do not reject Upper H 0 . There is sufficient evidence to conclude that the average utility bill in this state was lower in the winter of​ 2009-2010 than it was in the winter of​ 2008-2009.

D. Reject Upper H 0 . There is not sufficient evidence to conclude that the average utility bill in this state was lower in the winter of​ 2009-2010 than it was in the winter of​ 2008-2009.

​b) Does changing the value of alpha from 0.05 to 0.01 affect your​ conclusion? Why or why​ not?

A. Yes comma the conclusion changes. There is not sufficient evidence to reject Upper H 0.

B.No comma the conclusion does not change. There is sufficient evidence to reject Upper H 0.

C.No comma the conclusion does not change.There is not sufficient evidence to reject Upper H 0.

D.Yes comma the conclusion changes. There is sufficient evidence to reject Upper H 0 .

​c) Use technology to determine the​ p-value for this test.

​p-value=

​(Round to three decimal places as​ needed.)

Answer 1

Hypothesis 184 CYİ Hcal value O. 05, 39 74.91- 18 4 19-4 lm 14-0 1-2.95 Concluefon 3435 1-2. 426 0.01 39 e Concnim dos not Chomyn 10.003