Some researchers want to know how warm home owners keep thei

Some researchers want to know how warm home owners keep their houses in January and

how the results from Pennsylvania and New Jersey compare. The researchers randomly call 23

Pennsylvania households between 7.00 pm and 9.00 pm on January 20 and ask the respondent

how warm the house is according to the thermostat. The researchers then call 19 households in

New Jersey the same night and ask the same question. The following are the results:

Pennsylvania

71 71 65 68 70 61 67 69 75 68 71 73 74 68 67 69 69 72 67 72 70 73 72

New

Jersey

73 75 74 71 74 73 74 70 72 71 69 72 74 73 70 72 69 70 67

Use the calculator to do the following:

Using a level of significance of 0.01, is the average temperature of a house in Pennsylvania

higher than that of a house in New Jersey on the evening of January 20? Assume the population

variances are equal and the house temperatures are approximately normally distributed.

(a) State the null and the alternative hypotheses.

(b) Give the value of the test statistic, t.

(c) State the p-value.

(d) Give the decision and the conclusion in the context of the study.

(a) State the null and the alternative hypotheses.

Let mu1 be the mean for Pennsylvania

Let mu2 be the mean for New Jersey

Null hypothesis: mu1=mu2

Alternative hypothesis: mu1>mu2

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(b) Give the value of the test statistic, t.

n1=23, xbar1=69.65217, s1=3.156648

n2=19, xbar2=71.73684, s2=2.156182

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(69.65217-71.73684)/sqrt(3.156648^2/23+2.156182^2/19)

=-2.53

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(c) State the p-value.

It is a right-tailed test.

The degree of freedom =n1+n2-2=23+19-2 =40

So the p-value= P(t with df=40 >-2.53) =0.9923 (from student t table)

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(d) Give the decision and the conclusion in the context of the study.

Since the p-value is larger than 0.01, we do not reject the null hypothesis.

So we can not conclude that the average temperature of a house in Pennsylvania is

higher than that of a house in New Jersey on the evening of January 20