I want to research whether children who play a musical instrument performbetterin school than children who do not play an instrument (As a former marching band nerd, I might have some bias here, but I digress...). A sample (n= 16) of children who play a musical instrument had an average academic achievement score ofM= 87 withSS= 2940. Assume the average population academic achievement score for this age group is= 81.

Perform a one-sample t-test to determine whether children who play a musical instrument performbetterin school than children who do not play an instrument by stating or calculating each of the following:(Show your work or explain your answers for each!)

a. The null (H₀) and alternative (H_A) hypotheses. (4 points)

b. Whether we are using a one- or two-tailed test and why. (4 points)

c. Degrees of freedom (df) (3 points)

d. The critical/cut-offtstatistic using your degrees of freedom from the last step witha= .05. (4 points)

e. Sample variance (s²) (4 points)

f. Estimated standard error (s_M) (4 points)

g.t-statistic (4 points)

h. Based on our t-statistic and our critical t, are we rejecting or failing to reject the null hypothesis? What does that mean for our research question?(4 points)