Question

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. (x - y) 14 (a) The claim is that the mean difference (x - y) is more than 10 mm (ud > 10). What type of test is this? This is a two-tailed test. This is a left-tailed test. This is a right-tailed test. 9 (b) What is the test statistic? Round your answer to 2 decimal places. 12 10 13 15 (c) Use software to get the P-value of the test statistic. Round to 4 decimal places. P-value = 12 (d) What is the conclusion regarding the null hypothesis? reject Ho fail to reject Ho AM Height (x) PM Height (y) 1413 1405 1526 1512 1572 1565 1451 1442 1458 1450 1472 1458 1681 1667 1624 1612 1615 1605 1495 1482 1587 1572 1557 1545 1736 1723 1747 1733 1595 1584 1758 1741 1668 1653 1654 1634 1588 1579 1541 1533 1436 1427 1624 1612 1490 1480 1471 1463 1479 1471 1426 1417 1405 1393 1439 1433 1743 1734 1576 1563 11 17 15 20 (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. ROCCO

Answer 1

The statistical software output for this problem is:

One sample T hypothesis test: H: Mean of variable H -10 H > 10 Hypothesis test results: Variable Sample Mean Std. Err. DF T-Stat P-value 11.3 0.593354 29 21909349 0.0183

Hence,

a) Right Tailed Test

b) Test statistic = 2.19

c) P - value = 0.0183

d) Fail to Reject Ho

e) Option B is correct.