Question: An archaeology professor claims that the average floor space of Mesa Verde Anasazi kivas is µ = 12 sq. meters. However, it is stated that a random sample of 56 Mesa Verde Anasazi kivas had a sample mean area of \(\bar{X}\) = 12.3 sq. meters with sample standard deviation s = 3.4 sq. meters. Do these data indicate that the mean floor area of all such Mesa Verde kivas is different from µ = 12 sq. meters? Use \(\alpha =0.01\).

(a) Convert the sample mean \(\bar{X}\) to a sample z value. (Hint: due to the large sample size, approximate σ with s.)

(b) Sketch a graph of the z distribution. Show the location of the area corresponding to the P value for this test.

(c) Compute the P value for this test.

(d) Is the data significant at the specified level of significance \(\alpha =0.01\) ?