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 of30adults, 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 than10mm taller in the morning than at night. Test this claim at the0.05significance level.

(a) The claim is that the mean difference (x-y) is more than10mm (_d>10). What type of test is this?

This is a right-tailed test.

This is a two-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?

rejectH₀

fail to rejectH₀

(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)

1548 1541 7

1494 1481 13

1510 1503 7

1660 1650 10

1545 1537 8

1720 1707 13

1484 1470 14

1552 1541 11

1562 1552 10

1694 1681 13

1572 1558 14

1723 1711 12

1492 1478 14

1748 1732 16

1796 1787 9

1430 1414 16

1789 1774 15

1626 1608 18

1558 1549 9

1776 1767 9

1552 1542 10

1610 1600 10

1667 1659 8

1620 1611 9

1570 1562 8

1636 1627 9

1718 1705 13

1644 1638 6

1514 1504 10

1500 1488 12