Question: Data were collected on the heights of 41 children in a boarding school in India. For each child, the heights were measured (in mm) in the morning and again in the evening. The link to the AMPM-Heights data is given with this test. Researcher Peter Stothart noted that “We have known for well over a century that people are taller in the morning, shrink progressively through the day and recover their height overnight while sleeping.” Do these data support Stothart’s claim? Test the claim that children’s heights tend to decrease during the day. Use α = 0.05 level of significance to address this question.

(a) (2 points) State the appropriate statistical procedure.

(b) (2 points) Check the assumption that the sample size of the differences is large enough or the differences are normally distributed. (If graphs are needed, print these outputs from EXCEL and interpret)

(c) (2 points) What descriptive statistics would you use to describe the data (both numerical and graphical)? Please show the descriptive statistics (paste the correct graphic as part of your answer).

(d) (2 points) State the null and alternative hypotheses.

(e) (2 points) Report the test statistic and give its degrees of freedom.

(f) (2 points) State the P-value.

(g) (2 points) Sketch the sampling distribution, showing the test statistic and shading the P-value.

(h) (2 points) State your decision based on the decision rule.

(i) (2 points) Present your conclusion in an English sentence (in layman’s terms).