Question

x overbarx1	equals=	116116	x overbarx2	equals=	133133
sigmaσ1	equals=	3535	sigmaσ2	equals=	3939
n1	equals=	5555	n2	equals=	3535

Consider the hypothesis statement shown below using

alphaαequals=0.050.05

and the data to the right from two independent samples.

Upper H 0 : mu 1 minus mu 2 greater than or equals 0H0: μ1−μ2≥0

Upper H 1 : mu 1 minus mu 2 less than 0H1: μ1−μ2<0

​a) Calculate the appropriate test statistic and interpret the result.

​b) Calculate the​ p-value and interpret the result.

a) The test statistic is

. 37.37.

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

Determine the appropriate critical​ value(s).

The critical​ value(s) is(are)

1.6621.662.

​(Round to

threethree

decimal places as needed. Use a comma to separate answers as​ needed.)Since the test statistic

falls

falls

does not fall

in the rejection​ region,

do not reject

reject

do not reject

Upper H 0H0.

There is

insufficient

insufficient

sufficient

evidence to conclude that the mean of population 1 is less than the mean of population 2.​b) The​ p-value is

...

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

Since the​ p-value is

greater than

equal to

greater than

less than

alphaα​,

do not reject

do not reject

reject

Upper H 0H0.

There is

insufficient

sufficient

insufficient

evidence to conclude that the mean of population 1 is less than the mean of population 2.

Answer 1

a)test statistic=-2.10

appropriate critical​ value =-1.645

Since the test statistic falls in the rejection​ region, reject Ho. There is sufficient evidence to conclude that the mean of population 1 is less than the mean of population 2.

b) p-value =0.018

Since the​ p-value is less than α​, reject Ho. There is sufficient evidence to conclude that the mean of population 1 is less than the mean of population 2.