Tests and Confidence Intervals for One Sample

Problem 1.  Susan uses stable isotopes to study food webs.  One thing that she assumes is that the difference in delta15N between a consumer and its diet is 3.0 parts per thousand.  Given the following experimentally
determined differences in delta15N of consumers and their diets, is the
average difference really 3.0?

Let alpha = 0.05.  Also find a 95% confidence interval for the mean.

Measured differences:
2.7, 3.0, 3.1, 4.5, 2.2, 3.1, 3.7, 3.1, 2.7, and 2.9 parts per thousand

Answer help:  I got x-bar = 3.1, s^2 = 0.39, and t(obs) = 0.51.  The
confidence interval ranged from (2.6, 3.6).
______________________________________________________________

Problem 2.  A species of arthropod lives in seawater than contains
calcium in a concentration of 32 mmol/kg.  Thirteen animals are collected
and the calcium in their coelemic fluids are found to be:

28, 27, 29, 29, 30, 30, 31, 30, 33, 27, 30, 32, and 31 mmol/kg.

Test the appropriate null hypothesis to conclude whether this species
species maintains a coelemic calcium concentration lass than that of their
environment.  Let alpha(1) = 0.05.

Find a 95% confidence interval for the population variance.  Then find a
95% confidence interval for the population standard deviation.

Answer help:  I got x-bar = 29.77 and the sample variance to be 3.19.  I
got t(obs) = -4.46.  For the confidence intervals, I got (1.64 < sigma^2 <
8.69) and (1.28 < sigma < 2.95).