Question

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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 0.05 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 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) 1542 1535 7 1721 1709 12 1527 1520 7 1525 1515 10 1437 1431 6 1588 1576 12 1593 1580 13 1433 1422 11 1537 1525 12 1482 1470 12 1621 1607 14 1570 1559 11 1633 1619 14 1498 1484 14 1420 1411 9 1584 1567 17 1725 1711 14 1749 1729 20 1524 1515 9 1421 1411 10 1799 1791 8 1483 1472 11 1500 1492 8 1429 1422 7 1750 1744 6 1787 1778 9 1623 1611 12 1401 1393 8 1470 1460 10 1779 1766 13

Additional Materials

Answer 1

a)This is a right-tailed test

b)

test statistic t=(d-10)*sqrt(n)/std deviation =1.46

c)

P-value =0.0775

d)fail to reject H₀    

e)

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.