Can you help me solve this using R? 1. Medical research has shown that repeated interval for extensions beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at Cornell University used a proposed new computer mouse design, and while using the mouse, each student's wrist extension was recorded. ```{r} wrist <- data.frame(ID = 1:24, extension = c(27, 28, 24, 26, 27, 25, 25, 24, 24, 24, 25, 28, 22, 25, 24, 28, 27, 26, 31, 25, 28, 27, 27, 25)) ``` i) Compute the mean and standard deviation of the wrist extensions data above. Describe the sample using these summaries. ii) Create a histogram and QQ-plot of the wrist extensions. Is the normality assumption reasonable? iii) Use the data to estimate the mean wrist extension for people using this new mouse design using a 97\% confidence interval. Provide an interpretation of this interval. iv) Use the data to test the hypothesis that the mean wrist extension for people using this new design is greater than 20 degrees. Use alpha = 0.01 (1\%) level of significance.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...