In: Statistics and Probability
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. |
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Additional Materials
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.