Problem must be solved in RStudio.

a) Calculate the sample mean and standard deviation of P in the dataset below without using the built in functions mean, var, or sd. In other words, as we did manually in class, calculate these using only the primitive functions sum, division, subtraction, sqrt, and powers (e.g.xn). b) Next, we're going to test the following hypothesis: H0:H1:P=8P=8 Calculate the t-statistic for the test that the true population mean of P is =8. Again do this without using a built in function like t.test. You must do this using only the same primitive functions listed above