Question

During the winter of​ 2008-2009, the average utility bill for residents of a certain state was ​$172 per month. A random sample of 50

customers was selected during the winter of​ 2009-2010, and the average bill was found to be ​$162.37 with a sample standard deviation of ​$18.28.

answer the following below:

a.) Using alphaαequals=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.

b.) determine the critical value(s)

c.) determine the test statistic

d.) What conclusion should be​ drawn?

e.) ) Does changing the value of alphaα from 0.05 to 0.01 affect your​ conclusion? Why or why​ not?

f.) what is the p value for this test

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 172
Alternative Hypothesis, Ha: μ < 172

Rejection Region
This is left tailed test, for α = 0.05 and df = 49
Critical value of t is -1.677.
Hence reject H0 if t < -1.677

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (162.37 - 172)/(18.28/sqrt(50))
t = -3.725

Reject the null hypothesis.
There is significant 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

If alpha is change to 0.01, still the conclusion remains same.

P-value = 0.0003