Question

Provided below are summary statistics for independent simple random samples from two populations. Use the pooled​ t-test and the pooled​ t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.

x overbar 1x1equals=1414​,

s 1s1equals=2.42.4​,

n 1n1equals=1818​,

x overbar 2x2equals=1515​,

s 2s2equals=2.42.4​,

n 2n2equals=1818

a.​ Two-tailed test,

alphaαequals=0.050.05

b.

9595​%

confidence interval

a.​ First, what are the correct hypotheses for a​ two-tailed test?

A.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H Subscript aHa​:

mu 1μ1not equals≠mu 2μ2

Your answer is correct.

B.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H Subscript aHa​:

mu 1μ1less than<mu 2μ2

C.

Upper H 0H0​:

mu 1μ1less than<mu 2μ2

Upper H Subscript aHa​:

mu 1μ1equals=mu 2μ2

D.

Upper H 0H0​:

mu 1μ1greater than>mu 2μ2

Upper H Subscript aHa​:

mu 1μ1equals=mu 2μ2

E.

Upper H 0H0​:

mu 1μ1not equals≠mu 2μ2

Upper H Subscript aHa​:

mu 1μ1equals=mu 2μ2

F.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H Subscript aHa​:

mu 1μ1greater than>mu 2μ2

​Next, compute the test statistic.

tequals=nothing

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

Now determine the critical values.

plus or minus±t Subscript alpha divided by 2tα/2equals=plus or minus±nothing

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

What is the conclusion of the hypothesis​ test?

Since the test statistic

(1)

in the rejection​ region,

(2)

Upper H 0H0.

b. The

9595​%

confidence interval is from

nothing

to

nothing.

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

(1)

is

is not

(2)

reject

do not reject

Answer 1

compute the test statistic t=-1.250

critical values =-/+ 2.032

Since the test statistic is not in critical region fail to reject null hypothesis

b)

95​% confidence interval is from -2.626 to 0.626