Interpret your result. Is there evidence that the ecological footprint changed over that time? If so did it increase or decrease? 3. A common belief is that shaving causes hair to grow back faster or coarser than it was before. Is this true? Lynfield and McWilliams (1970) did a small experiment to test for an effect of shaving. Five men shaved one leg weekly for several months while leaving the other leg unshaved. (The data from the shaved leg has the word "test" in the variable name,- the data from the unshaved leg is labeled with "control.") At the end of the experiment, the researchers measured the difference in leg hair width and the hair growth rate on each of the legs. These data are given in "leg shaving.csv". a. Perform a suitable hypothesis test to determine whether shaving affects hair thickness. b. How big is the difference? Find the 95% confidence interval for the difference between shaved and unshaved legs for hair thickness. 4. During the last lab, you had measured your fingers. We're going to use these data now. We'll look at the ratio of the lengths of index finger over ring finger. This is called the 2D:4D ratio, where the 2D refers to second digit and 4D means fourth digit. It turns outbizarrelythat this 2D:4D ratio is a measure ofthe amount of testosterone that a fetus is exposed to during gestation. As such, we might expect there to be a difference between males and females in the 2D:4D ratio. We'll also estimate the 2D:4D ratio, and ask whether its mean is significantly different from 1. If index fingers are equal to ring fingers in length, then the ratio would be one. First, use the finger data file found on Canvas. Note that I already looked through the measurements and corrected three cases of clearly wrong punctuation (e.g. 720 instead of72.o or 4.9 instead of 49), and deleted five unrealistically large measurements of 120 mm or more. Create a new vector called "Right_2D_1,D_ratio". In this vector, calculate the ratio of the length of the index finger over the length of the ring finger for each individual. a. Describe how well the "Right_2D_4D_ratio" is fit by a normal distribution, by usin g both ofthe two methods we have learned this week. b. What is the 95% confidence interval for "Right_2D_4D_ratio"? c. Make an appropriate graph to show the relationship between gender and 2D:4D ratio of the right hand. Does it look like variances are equal between the two genders? d. Test fora difference in the mean 2D:1,D ratio between men and women. e. What is the magnitude of the difference? Compute the 95% confidence interval for the difference in means