Question

According to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Denmark. A new study has been made to see whether this has changed. Records of

225

individuals from the United States who died recently are selected at random. The

225

individuals lived an average of

77.7

years with a standard deviation of

7.8

years. Records of

295

individuals from Denmark who died recently are selected at random and independently. The

295

individuals lived an average of

75.9

years with a standard deviation of

6.1

years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the

0.05

level of significance, is there enough evidence to support the claim that the life expectancy,

μ1

, in the United States is greater than the life expectancy,

μ2

, in Denmark? Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one)ZtChi squareF (give degree of freedom if other than Z)
The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.05 level of significance: (Round to at least three decimal places.)
Can we support the claim that the life expectancy in the United States is greater than the life expectancy in Denmark?		Yes	No

Answer 1

1)

null hypothesis: Ho:μ1<=μ2

Alternate hypothesis: Ha:μ1 >μ2

2)

type of test statistic =z

3)

x1            =	77.70	x2            =	75.90
n1           =	225	n2           =	295
σ1           =	7.80	σ2           =	6.10
std error σx1-x2=√(σ21/n1+σ22/n2)    =			0.630
test stat z =(x1-x2-Δo)/σx1-x2     =			2.859

4)

critical value =1.645

5)

Yes since test statistic >critical value