Activity:
More on Hypothesis Tests
1. The
makers of Sport Flakes cereal want to make sure that the machine that puts
the flakes into the boxes is working correctly. The
box label states that there are 12.0 ounces of cereal in the box.
(a) Which
one of the following research questions is most appropriate for the Quality
Control Dept.at this company?
A. On
average, do these boxes contain less than 12.0 ounces of cereal?
B. On
average, do these boxes contain more than 12.0 ounces of cereal?
C. Is
the average amount of cereal per box different from 12.0?
(b) Give
the alternative hypothesis using symbols corresponding to each of the RQ’s
above.
A. B. C.
(c) State
the null hypothesis both in words and symbols.
(d) A
consumer group is suing the makers of Sport Flakes cereal. They
claim that the company is cheating consumers by underfilling its boxes. Which
of the RQ’s in (a) is appropriate for the consumer group?
2. Suppose
the consumer group takes a random sample of 36 boxes and finds a sample
mean of 11.5. Assume that
the standard deviation for individual boxes is s
= 0.8.
(a) Determine
the Z-score for a mean of 11.5, if the population mean is actually 12.0,
as advertised.
(b) Give
the P-value.
(c) State
a conclusion.
3. Repeat
#2 for a sample of 36 boxes and a sample mean of 11.95.
(a)
(b)
(c)
4. Repeat
#2 for a sample of 3600 boxes and a sample mean of 11.95.
(a)
(b)
(c)
5. Summary
of results for the above cases (#2, 3, 4).
(a) In
which of these cases did you find a “statistically significant” result
(i.e., a P-value below .05)?
(b) In
which of these cases do you think that the difference between the actual
amount of flakes in the box and the advertised amount is substantial enough
to merit legal action against the maker of Sport Flakes?