Question

7. 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 30adults, 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 left-tailed test.This is a right-tailed test.     This is a two-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) 1609 1600 9 1770 1757 13 1563 1556 7 1599 1588 11 1659 1652 7 1561 1548 13 1621 1607 14 1401 1390 11 1440 1430 10 1693 1680 13 1467 1453 14 1667 1655 12 1736 1723 13 1424 1409 15 1785 1774 11 1585 1567 18 1472 1459 13 1629 1609 20 1409 1398 11 1481 1471 10 1589 1580 9 1499 1487 12 1532 1524 8 1507 1498 9 1445 1439 6 1637 1629 8 1658 1644 14 1680 1674 6 1799 1790 9 1436 1423 13

Answer 1

a) This is a right-tailed test.

b) - d)

e) 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.