Names of Group Members (In Attendance!)

STAT 110: Bonus Assignment (pts.) - Due Sunday, November 24th

Names of Group Members (in attendance!):

1 – Wingspan and Height Comparisons with Gender

It is believed that a person’s height should be the same is their wingspan. This was demonstrated in a famous sketch by Leonardo Da Vinci called the Vitruvian Man.

Research Question: Is there evidence that wingspan and height have a mean difference different from zero when measured on the same person?

To answer this question we will have a measurement team that will measure everyone’s wingspan and height in inches.

Once we have measured both of these quantities can compute the Difference = Height – Wingspan.

We will also record the gender of each subject so we can examine any potential gender differences in these quantities and in the difference between height and wingspan.

Questions

If on average the height (in.) and wingspan (in.) are the same in the population of adults, what do expect the mean of the variable Difference defined above to be? Explain. (2 pts.)
Form the differences between the height (in) and wingspan (in) and compute summary statistics and obtain a histogram & boxplot of these differences. Copy and paste these into the assignment. Use the summary statistics and graphical displays to summarize the differences between height (in) and wingspan (in) the sample. (4 pts.)
Do the differences appear to be normally distributed? Explain. (2 pts.)

Again the research question is:
Is there evidence that wingspan and height have a mean difference differentfrom zero when measured on the same person?

State Ho and Ha in words and in terms of the mean difference (). (3 pts.)
Check assumptions required for using a t-test, do they appear to be satisfied for these data? (1 pt.)

Conduct a test that allows you answer the research question and state your conclusion. (3 pts.)

Construct a 95% CI for the mean difference between the height and wingspan for the population of adults. Interpret this interval. Does this interval agree with your results from the hypothesis test? Explain. (4 pts.)

Males – repeat (4) – (8) for the population of males

a) State Ho and Ha in words and in terms of the mean difference ((2 pts.)

b) Check assumptions required for using a t-test, do they appear to be satisfied for these data? (1 pt.)

c)Conduct a test that allows you answer the research question and state your conclusion. (3 pts.)

d)Construct a 95% CI for the mean difference between the height and wingspan for the population of adult males. Interpret this interval. (3 pts.)

Females – repeat (4) – (8) for the population of females

a)State Ho and Ha in words and in terms of the mean difference ((2 pts.)

b) Check assumptions required for using a t-test, do they appear to be satisfied for these data? (1 pt.)

c)Conduct a test that allows you answer the research question and state your conclusion. (3 pts.)

d)Construct a 95% CI for the mean difference between the height and wingspan for the population of adult females. Interpret this interval. (3 pts.)

Do the results for males and females differ? If so, how? (2 pts.)

Add a new column and call it “W > H” to the spreadsheet and type Y if the persons Wingspan is greater than their height, type N if the persons Height is greater than their Wingspan and leave it blank if the measurements are the same.

a) Conduct a test to determine if there is a relationship between Gender and W > H. Summarize your findings. (6 pts.)