Question

A researcher randomly selects 6 fathers who have adult sons and records the​ fathers' and​ sons' heights to obtain the data shown in the table below. Test the claim that sons are taller than their fathers at the

alpha equals 0.10α=0.10

level of significance. The normal probability plot and boxplot indicate that the differences are approximately normally distributed with no outliers so the use of a paired​ t-test is reasonable.

Observation	1	2	3	4	5	6
Height of father​ (in inches)	73.5	69.1	71.1	73.5	71.6	65.8
Height of son​ (in inches)	74.8	67.3	69.5	72.8	75.7	68.4

What are the hypotheses for the​ t-test? Note that population 1 is fathers and population 2 is sons.

A.

H0​:

muμ1equals=muμ2

Ha​:

muμ1less than<muμ2

B.

H0​:

muμ1greater than or equals≥muμ2

Ha​:

muμ1less than<muμ2

C.

H0​:

muμ1equals=muμ2

Ha​:

muμ1greater than>muμ2

D.

H0​:

muμ1equals=muμ2

Ha​:

muμ1not equals≠muμ2

Find the test statistic.

tequals=nothing

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

Find the critical​ value(s).

The critical​ value(s) is/are

nothing.

​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

What is the correct conclusion for the hypothesis​ test?

A.

Do not rejectDo not reject

Upper H 0H0.

There

is notis not

sufficient evidence that sons are taller than their fathers.

B.

Do not rejectDo not reject

Upper H 0H0.

There

isis

sufficient evidence that sons are taller than their fathers.

C.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence that sons are taller than their fathers.

D.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence that sons are taller than their fathers.

Click to select your answer(s).

Answer 1

from above:

What are the hypotheses for the​ t-test? option A is correct

test statistic t =-0.661

critical​ value(s) is t = -1.476

correct conclusion for the hypothesis​ test? option A is correct