A study was done to test the notion that people are taller when they first wake up in the morning than in the evening right before they go to bed. To test this theory, the heights of children in a boarding school in India were measured. Values were recorded (in mm) for each child in the morning and again in the evening. The data is recorded in AMPM-Heights. xlsx (Links to an external site.). 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. Required:
a. 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 α= 0.05. Is the alternative hypothesis for this test one-tailed or two-tailed?
b. Give the test statistic for this test. Round your answer to the three decimal places
c. Give the degrees of freedom for this test.
d. What is the P-value for this test?