Question

Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed. ​(a) Test whether mu 1μ1greater than>mu 2μ2 at the alphaαequals=0.050.05 level of significance for the given sample data.​(b) Construct a 9595​% confidence interval about mu 1μ1minus−mu 2μ2.			Population 1	Population 2
		n	2525	1919
		x overbarx	47.547.5	40.740.7
		s	5.75.7	10.710.7

​(a) Identify the null and alternative hypotheses for this test.

A.

Upper H 0H0​:

mu 1μ1less than<mu 2μ2

Upper H 1H1​:

mu 1μ1equals=mu 2μ2

B.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H 1H1​:

mu 1μ1less than<mu 2μ2

C.

Upper H 0H0​:

mu 1μ1not equals≠mu 2μ2

Upper H 1H1​:

mu 1μ1equals=mu 2μ2

D.

Upper H 0H0​:

mu 1μ1greater than>mu 2μ2

Upper H 1H1​:

mu 1μ1equals=mu 2μ2

E.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H 1H1​:

mu 1μ1not equals≠mu 2μ2

F.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H 1H1​:

mu 1μ1greater than>mu 2μ2

Find the test statistic for this hypothesis test.

nothing

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

Determine the​ P-value for this hypothesis test.

nothing

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

State the conclusion for this hypothesis test.

A.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence at the

alphaαequals=0.050.05

level of significance to conclude that

mu 1μ1greater than>mu 2μ2.

B.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence at the

alphaαequals=0.050.05

level of significance to conclude that

mu 1μ1greater than>mu 2μ2.

C.

Do not rejectDo not reject

Upper H 0H0.

There

is notis not

sufficient evidence at the

alphaαequals=0.050.05

level of significance to conclude that

mu 1μ1greater than>mu 2μ2.

D.

Do not rejectDo not reject

Upper H 0H0.

There

isis

sufficient evidence at the

alphaαequals=0.050.05

level of significance to conclude that

mu 1μ1greater than>mu 2μ2.

​(b) The

9595​%

confidence interval about

mu 1μ1minus−mu 2μ2

is the range from a lower bound of

nothing

to an upper bound of

nothing.

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

Answer 1

follow the following steps to do the hypothesis testing

follow the following steps for confidence interval calculation