10.19

a) x=13.5

b) The degrees of freedom is 35. The value of t*  from the table could be 2.042(using 30 degrees of freedom), or 2.021(using 40 degrees of freedom), or
use z* = 1.96 or 2 (based on 68-95-99.7 rule)

The confidence interval is 13.5 +/- 2.1*2.042 or replace 2.042 by 2.021 or 2 or 1.96. All these give similar confidence intervals.

c)if we repeat this method over and over, yielding many 95% confidence intervals for u, we expect

95% of these intervals to contain the true parameter value.

10.25

Student 4's answer is correct.

10.26

The correct answer is (c).
 

11.6
(a) Study 1 (independent Sample): take a random sample of freshman and compare to a random sample of sophomore, see the percentage of seeking advice from academic advisor.
       Study 2 (paired sample): take a sample of academic advisors, compare the number of freshmen advisee with the number of sophomore advisees

(b) Independent Sample: randomly select two groups of students, one group will go through the prep course before take SAT,  the
other group take the exam without the prep courses.

(c) Paired design: take a sample of pairs of twins, measure the difference in height of each pair.