Teachers at all levels believe that an increase in study time correlated with higher grades. A random sample of 23 statistics students from students taking AP statistics in 2013 gave the following number of hours studying for the exam:

13.48, 5.45, 14.23, 7.33, 12.15, 11.49, 12.78, 11.74, 6.65, 9.08, 11.86, 6.80, 10.65, 10.69, 10.64, 12.44, 9.82, 6.92, 10.15, 8.78, 6.18, 12.22, 9.77

Hours studying for an exam are known to be normally distributed. with unknown mean ofhours and an unknown standard deviationhours

a) Calculate the sample median for this data.

b) Calculate the sample mean for this data..

c) Calculate the sample standard deviation for this data.

d) Calculate the maximum likelihood estimate for²

using this data.

e) Calculate an unbiased estimate for²

using this data.

f) Suppose W has a t distribution with 22 degrees of freedom. If P(W > t) = .01 then what is t?

g) Suppose W has a t distribution with 22 degrees of freedom. If P(W < t) = .01 then what is t?

h) Calculate the 99th percentile of a standard normal distribution.

i) Compute an 99% Confidence Interval forusing your answers above.,

j) Compute an 99% Prediction Interval for a single future subject's study hours measurement using your answers above..,

k) Copy your R script or other comments for the above into the text box here.