Question

In: Statistics and Probability

AM -vs- PM Height (Raw Data, Software Required): It is widely accepted that people are a...

AM -vs- PM Height (Raw Data, Software Required):
It is widely accepted that people are a little taller in the morning than at night. Here we perform a test on how big the difference is. In a sample of 30 adults, the morning height and evening height are given in millimeters (mm) in the table below. Use this data to test the claim that, on average, people are more than 10 mm taller in the morning than at night. Test this claim at the 0.01 significance level.



(a) The claim is that the mean difference (x - y) is more than 10 mm (μd > 10). What type of test is this?

This is a two-tailed test.This is a right-tailed test.    This is a left-tailed test.


(b) What is the test statistic? Round your answer to 2 decimal places.
t

d

=

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H0fail to reject H0    


(e) Choose the appropriate concluding statement.

The data supports the claim that, on average, people are more than 10 mm taller in the morning than at night.There is not enough data to support the claim that, on average, people are more than 10 mm taller in the morning than at night.    We reject the claim that, on average, people are more than 10 mm taller in the morning than at night.We have proven that, on average, people are more than 10 mm taller in the morning than at night.

    
    
AM Height (x) PM Height (y) (x - y)
1584 1575 9
1429 1416 13
1502 1494 8
1477 1468 9
1766 1758 8
1598 1586 12
1490 1478 12
1768 1755 13
1696 1684 12
1557 1545 12
1432 1418 14
1753 1743 10
1786 1772 14
1719 1704 15
1752 1742 10
1683 1667 16
1598 1585 13
1714 1696 18
1459 1449 10
1683 1674 9
1685 1676 9
1484 1472 12
1762 1754 8
1481 1472 9
1656 1649 7
1669 1660 9
1542 1529 13
1585 1579 6
1728 1719 9
1571 1560 11

Additional Materials

Solutions

Expert Solution

Sol:

Ho:(μd <=10

Ho:(μd > 10

AM Height (x)   PM Height (y)   (x - y)
1584   1575   9
1429   1416   13
1502   1494   8
1477   1468   9
1766   1758   8
1598   1586   12
1490   1478   12
1768   1755   13
1696   1684   12
1557   1545   12
1432   1418   14
1753   1743   10
1786   1772   14
1719   1704   15
1752   1742   10
1683   1667   16
1598   1585   13
1714   1696   18
1459   1449   10
1683   1674   9
1685   1676   9
1484   1472   12
1762   1754   8
1481   1472   9
1656   1649   7
1669   1660   9
1542   1529   13
1585   1579   6
1728   1719   9
1571   1560   11
Md   11
Sd   2.803938117
n   30

.This is a right-tailed test.   

.This is a right-tailed test.   

b) What is the test statistic? Round your answer to 2 decimal places.
t=(Md-mu)/(sd/sqrt(n))

t=(11-10)/(2.803938117/sqrt(30))

=1.953405

t=1.95

d=n-1=30-1=29

ANSWER:

T=1.95

d=29

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.

=T.DIST.RT( 1.953405,29)

=0.030239921

p=0.0302

ANSWER:
P-value =0.0302

(d) What is the conclusion regarding the null hypothesis?

alpha=0.01

0.0302>0.01

p>alpha

fail to reject H0    

fail to reject H0    

(e) Choose the appropriate concluding statement.

There is not enough data to support the claim that, on average, people are more than 10 mm taller in the morning than at night.


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