Problem 23.3 t-models, part III. As the number of degrees of
freedom increases, the centres of t-models do not change. The
spread of t-models decreases as the number of degrees of
freedom increases, and the shape of the distribution becomes
closer to Normal.
Problem 23.7 Meal plan.
a)Not correct. The confidence interval is not about the individual
students in the population.
b) Not correct. The confidence interval is not about individual
students in the sample. In fact, we know exactly what these
students spent, so there is no need to estimate.
c)Not correct. We know that the mean cost for students in this
sample was $1196.
d) Not correct. A confidence interval is not about other sample
e) This is the correct interpretation of a confidence interval. It
estimates a population parameter.
Problem 23.9 Pulse rates.
a)We are 95% confident the interval 70.9 to 74.5 beats per
minute contains the true mean heart rate.
b) The width of the interval is about 74.5 – 70.9 = 3.6 beats per
minute. The margin of error is half of that, about 1.8 beats
c)The margin of error would have been larger. More confidence
requires a larger critical value of t, which increases the margin
Problem 23.15. Normal temperatures, part II.
a)The 90% confidence interval would be narrower than the 98%
confidence interval. We can be more precise with our interval
when we are less confident.
b) The 98% confidence interval has a greater chance of
containing the true mean body temperature of adults than the
90% confidence interval, but the 98% confidence interval is
less precise (wider) than the 90% confidence interval.
c)The 98% confidence interval would be narrower if the sample
size were increased from 52 people to 500 people. The
smaller standard error would result in a smaller margin of
d) Our sample of 52 people gave us a 98% confidence interval
with a margin of error of (36.96 – 36.7)/2 =0.13°C. In order to
get a margin of error of 0.05, less than half of that, we need a
sample over 4 times as large. It should be safe to use t