Statistics and Estimates with Least Squares Line

The number of words was noted in each of 100 sentences selected at random from two political thrillers written by different authors; 50 sentences were selected from each book. A summary of the data is given in the table (see attachment).

The two-sample z-test is to be used to investigate whether there is a difference, at the 5% significance level, between the mean length of sentences in the book by author A and the mean length of sentences in the book by author B.

21. choose the option that gives, to two decimal places, the estimated standard error of the difference between the two population means.
A 0.45 B 0.79 C 1.10 D 3.18 E 6.01 F 10.10

22. Choose the two options that give the value to two decimal places of the magnitude of the test static z, and the construction obtained from the test.
A 0.25 B 0.56 C 0.64 D 0.79 E 3.01 F 3.63
G There seems to be a significant difference, at the 5% significance level, between the mean sentence length in the book by author A and that in the book by author B.
H There seems to be no significant difference, at the 5% significance level, between the mean sentence length in the book by author A and that in the book by author B.

In the article 'Some physical properties of lentil seeds' by K. Carman (Journal of Agricultural Engineering Research, vol. 63, no. 2, pp. 87-92, 1996), the relationship between the moisture content and projected area of lentil seeds is modelled by a least square fit line. (The projected area of a seed is the area of its shadow on a plane surface when the light rays are perpendicular to the surface.) The least square fit line has equation y = 52.16 + 0.964x, where x is the moisture content in %d.b. (dry basis) and y is the projected area in mm^2.

23. Choose the option that, according to this model, is closest to the predicted projected area of a lentil seed with moisture content 15% d.b.
A 37.7 B 38.55 C 52.16 D 53.12 E 66.62 F 783.36

24. Suppose that the moisture content of lentil seed A is 10% d.b. greater than the moisture content of lentil seed B. Choose the option that, according to this model, is closest to the predicted amount (in mm^2) by which the projected area of the lentil seed A exceeds that of lentil seed B.