It is widely accepted that people are a little taller in the morning than at nig

Question

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.

This is a right-tailed test.

This is a left-tailed test.    

This is a two-tailed test.

reject H0

fail to reject H0    

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.

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

This is a right-tailed test.

This is a left-tailed test.    

This is a two-tailed test.

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

(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 H0

fail 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) 1531 1522 9 1725 1713 12 1596 1587 9 1428 1418 10 1509 1502 7 1674 1660 14 1718 1704 14 1652 1641 11 1547 1537 10 1755 1744 11 1797 1783 14 1455 1443 12 1690 1677 13 1632 1618 14 1497 1488 9 1633 1617 16 1790 1777 13 1576 1557 19 1574 1565 9 1712 1703 9 1572 1564 8 1624 1614 10 1576 1566 10 1595 1586 9 1454 1447 7 1723 1714 9 1515 1501 14 1555 1548 7 1730 1722 8 1573 1560 13

Explanation / Answer

This is a right-tailed test.

t stat =0.20

p value=0.43

fail to reject

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.

AM Height (x) PM Height (y) (x - y) 1531 1522 9 1725 1713 12 1596 1587 9 1428 1418 10 1509 1502 7 1674 1660 14 1718 1704 14 1652 1641 11 1547 1537 10 1755 1744 11 1797 1783 14 1455 1443 12 1690 1677 13 1632 1618 14 1497 1488 9 1633 1617 16 1790 1777 13 1576 1557 19 1574 1565 9 1712 1703 9 1572 1564 8 1624 1614 10 1576 1566 10 1595 1586 9 1454 1447 7 1723 1714 9 1515 1501 14 1555 1548 7 1730 1722 8 1573 1560 13 mean 10.500 std deviaition 3.5355 std error= std dev/(n)^(1/2) 2.5000 t stat= (d-10)/std error 0.2000 p value = 0.4300

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