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6.2 Stuff
If the distribution of a random variable x is
approximately normal, then
follows a t-distribution.
Critical values of t are denoted by tc
6.2 Stuff
The t-distribution has the following properties:
1. The t-distribution is bell shaped and symmetric about the mean.
2. The total area under a t-curve is 1 or 100%.
3. The mean, median, and mode of the t-distribution are equal to
4. The t-distribution is a family of curves, each determined by a
parameter called the degrees of freedom. When you use a
t-distribution to estimate a population mean, the degrees of
freedom are equal to one less than the sample size (n – 1).
5. As the degrees of freedom increase, the t-distribution
approaches the normal distribution.
6.2 Exercise #18
In a random sample of five people, the mean driving
distance to work was 22.2 miles and the sample
standard deviation was 5.8 miles.
Assume the random variable is normally distributed.
Construct a 95% confidence interval for the
population mean.
6.2 Exercise #27
In a random sample of 50 people, the mean body
mass index (BMI) was 27.7 and the standard
deviation was 6.1. Assume the body mass indexes
are normally distributed.
6.2 Exercise #28
In a random sample of 15 mortgage institutions, the
mean interest rate was 4.99% and the standard
deviation was 0.36%. Assume the interest rates are
normally distributed.
6.2 Exercise #30
In a recent season, the standard deviation of the
yards per carry for all running backs was 1.34. The
yards per carry of 20 randomly selected running
backs are listed below. Assume the yards per carry
are normally distributed.
5.6 4.4 3.8 4.5 3.3 5.0 3.6 3.7 4.8 3.5
5.6 3.0 6.8 4.7 2.2 3.3 5.7 3.0 5.0 4.5