Question

# A study was done on skull sizes of humans during different time periods. The results are...

 4000 B.C. A.D. 150 A study was done on skull sizes of humans during different time periods. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. muμ mu 1μ1 mu 2μ2 n 3030 3030 x overbarx 132.01132.01 mm 135.49135.49 mm s 5.035.03 mm 5.275.27 mm

a. Use a

0.010.01

significance​ level, and test the claim that the mean skull breadth in 4000 B.C is less than the mean skull breadth in A.D 150.

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H 1H1​:

mu 1μ1not equals≠mu 2μ2

B.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H 1H1​:

mu 1μ1greater than>mu 2μ2

C.

Upper H 0H0​:

mu 1μ1equals=mu 2μ2

Upper H 1H1​:

mu 1μ1less than<mu 2μ2

D.

Upper H 0H0​:

mu 1μ1not equals≠mu 2μ2

Upper H 1H1​:

mu 1μ1less than<mu 2μ2

The test​ statistic, t, is

nothing .

​(Round to two decimal places as​ needed.)The​ P-value is

nothing .

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

State the conclusion for the test.

A.

RejectReject

the null hypothesis. There

isis

sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

B.

RejectReject

the null hypothesis. There

is notis not

sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

C.

Fail to rejectFail to reject

the null hypothesis. There

is notis not

sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

D.

Fail to rejectFail to reject

the null hypothesis. There

isis

sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

b. Construct a confidence interval suitable for testing the claim that the mean skull breadth in 4000 B.C is less than the mean skull breadth in A.D 150.

nothing less than<mu 1 minus mu 2μ1−μ2less than<nothing

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

Does the confidence interval support the conclusion of the​ test?

Yes,

No,

because the confidence interval contains

zero.

only negative values.

only positive values.

(A)we have to test whether the mean skull breadth in 4000 B.C is less than the mean skull breadth in A.D 150.

So, it is a left tailed hypothesis

option C is correct hypothesis

Using TI 84 calculator

STAT>TESTS>2-SampTTest

Pooled: NO

ENTER

test statistic t = -2.62

p value = 0.006

p value is less than 0.01 significance level, so we can reject the Ho

Reject null hypothesis. There is sufficient evidence to support the claim that the mean skull breadth was less in 4000 B.C. than A.D. 150.

(B) Using TI 84 calculator

STAT>TESTS>2-SampTInt

Pooled: NO

c-level = 0.99

(-7.023, 0.063)

Yes, because the confidence interval contains zero.

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