The length of the skulls of 10 fossil skeletons of an extinct species of bird has a sample mean of 5.68 cm and a sample standard deviation of 0.29 cm. Assume that the 10 data collection random...

The length of the skulls of 10 fossil skeletons of an extinct species of bird has a sample mean of 5.68 cm and a sample standard deviation of 0.29 cm. Assume that the 10 data collection random variables are lid N(IIA,C A) .
(a)(5pts) Use the appropriate statistic in Table 1 to arrive at a 90% 2-sided CI estimate. Solution: [See code @. 2(a).]
(13)(5Pts) Consider the hypothesis test H0: lax = 5.5 vs- H, : p1 *5.5- Carry out the test for false alarm probability a = 0.1. Solution: [See code @. 2(a).]
(c)(5pts) How does = 5.5 relate to your CI estimate in (a). Answer:
(dX5pts) Find thep-value of the test in (b). Solution: (e)(5pts) 106 simulations of {C}1,1, = 5.68,a1 = 0.29) to arrive at a scatter plot of the 2D random variable (j11, 6A). (ii) Use the `smscgc,f command to estimate the correlation, Lt, between these two random variables. (iii) Explain whether your value for p makes sense, in view of your scatter plot. Solution: [See code @. 1(d).] (i): See plot @ right. (ii):