You want to determine if the children are taller in the morning than in the evening. Define the differences as AM Height minus PM Height. Compute a 95% confidence interval for the true mean difference of heights. Input your answers below.student - am height - pm height1 1728.75 1720.25 The heights of children in a boarding school in India were measured. Values2 1538.25 1528.50 were recorded (in mm) for each child in the morning and again in the evening.3 1462.25 1452.50 4 1782.50 1776.50 Source:5 1671.00 1667.00 Curtis A. & Trumbo B. Shrinking Students, Poisoned Children, and Bootstraps.6 1581.75 1571.00 Stats The Magazine for Students of Statistics, 47:??.7 1673.75 1664.50 8 1721.75 1708.50 9 1646.50 1636.00 10 1793.75 1781.75 11 1825.25 1814.00 12 1801.50 1787.00 13 1742.50 1729.75 14 1720.50 1711.50 15 1728.25 1717.25 16 1753.75 1742.75 17 1725.50 1716.75 18 1598.00 1592.25 19 1756.25 1747.00 20 1674.00 1662.50 21 1688.75 1677.00 22 1688.75 1681.00 23 1620.75 1613.50 24 1679.00 1668.25 25 1557.25 1550.25 26 1704.50 1696.50 27 1632.75 1619.00 28 1587.00 1581.50 29 1598.75 1590.50 30 1592.25 1583.50 31 1719.50 1709.25 32 1807.50 1795.00 33 1624.00 1619.50 34 1705.25 1694.50 35 1692.75 1686.00 36 1795.25 1782.00 37 1643.50 1628.75 38 1677.25 1668.25 39 1647.75 1641.50 40 1620.00 1608.25 41 1727.50 1721.25 For a 95% confidence interval for the true mean difference of height, find the margin of error (Round your answer accurate to three decimal places).Input the lower bound. (Round your answer accurate to three decimal places)Input the upper bound. (Round your answer accurate to three decimal places)You also want to conduct a hypothesis test to determine if heights are taller in the morning than in the evening. Use a level of significance of ?=0.05Is the alternative hypothesis for this test one-tailed or two-tailed?Give the test statistic for this test. (Round your answer to the three decimal places)Give the degrees of freedom for this test.What is the P-value for this test? (Round your answer to three decimal places)Based on your results of this test, is there enough evidence to suggest that the children are taller in the morning than in the evening?

Each student's height was twice as paired t test will be used. The result of the t test paired with a trust interval of 95 percent produced by Excel is the following:

The 95% confidence interval is (8.728, 10.455)

The margin of error: 0.864

Lower bound: 8.728

Upper bound: 10.455

Let d =morning - evening

Hypotheses are:

H_{0}:\mu_{d}=0,H_{a}:\mu_{d}>0

The test statistics is

t = 22.446

The df is: df= 40

The p-value is:

p-value= 0.0000

The evidence suggests that the kids are taller in the morning than in the night.