SECTION 6.5 Hypothesis Testing 403
represents taking two independent samples; we won’t go into the appro-
priate statistic for evaluatingH 0. On the other hand, the matched-pairs
design is easier; all one needs to do is to compute the difference of the
two effects. IfXis the random variable representing the difference, and
ifμX is the mean ofX, then we are simply evaluatingH 0 : μX = 0
against an appropriately-chosen alternative. The methods of the above
sections apply immediately.
Exercises
- The TI calculator command randNorm(0,1) generates a random
number from a normal distribution with mean 0 and variance 1.
Do you believe this? The command
randNorm(0, 1 ,100)−→L 1
will put 100 independent samples of this distribution into the list
variable L 1. Test the hypothesis μ = 0 at the 99% significance
level.2.^29 Sarah cycles to work and she believes that the mean time taken
to complete her journey is 30 minutes. To test her belief, she
records the times (in minutes) taken to complete her journey over
a 10-day period as follows:
30.1 32.3 33.6 29.8 28.9 30.6 31.1 30.2 32.1 29.4
Test Sarah’s belief, at the 5% significance level.- Suppose it is claimed that 80% of all SAS graduating seniors go
on to attend American Universities. Set up null and alternative
hypotheses for testing this claim. - Suppose instead it is claimed that at least 80% of all SAS gradu-
ating seniors go on to attend American Universities. Set up null
and alternative hypotheses for testing this claim.
(^29) From IB Mathematics HL Examination, May 2006, Paper 3 (Statistics and Probability), #3.