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9.2 Notes
Tests Involving µ
Procedure for Hypothesis Testing when σ is known
1) Establish the ______ Hypothesis (____)
2) Establish the ____________ Hypothesis (_______)
3) Use _____ to determine location of critical region (____________, ________
________, or ___________)
4) Use ___ and __________ to determine the critical value(s) for the critical
region
5) Using Z-Test in calc., calculate the statistical value based on the sample
6) Based on statistical value, draw your conclusions
1) Reject H0 - (We are ?% confident that H1, therefore …)
2) Fail to reject H0 - (At the ?% level of significance the evidence is not
strong enough to imply H1, therefore …)
Ex. 1 The St. Louis Zoo wishes to obtain eggs of a rare Mississippi river turtle.
The zoo will hatch the eggs and raise the turtles as an exhibit of a rare and
endangered species. Past research has shown that lengths of turtle eggs are
normally distributed, and lengths of the rare turtle eggs have μ = 7.50 cm with σ
= 1.5 cm. Then mean lengths of all other turtle eggs in the area are longer than
7.50 cm with similar deviation. A biologist found an abandoned nest of 36 eggs
that have a mean length x = 7.74 cm. Because a lot of effort goes into
removing and incubating the eggs, the biologist is a little concerned that the
eggs may be from another species that lays larger eggs. Should the biologist
bother to remove and incubate the eggs? Test at the 1% level of significance.
Ex. 2 A research meteorologist has been studying wind patterns over the
Pacific Ocean. Based on these studies, a new route is proposed for commercial
airlines going from San Francisco to Honolulu. The new route is intended to
take advantage of existing wind patterns to reduce flying time. It is known that
for the old route the distribution of flying times for a large four-engine jet has
mean μ = 5.25 hours with standard deviation σ = 0.6 hour. Thirty-six flights on
the new route have yielded a mean flying time of 4.90 hours. Should the
company adopt the new flight path? Test at the 5% level of significance.
Ex. 3 A machine makes twist-off caps for bottles. The machine is adjusted to
make caps of diameter 1.85 cm. Production records show that when the
machine is so adjusted, it will make caps with mean diameter 1.85 cm and with
standard deviation σ = 0.05 cm. During production, an inspector checks the
diameters of caps to see if the machine has slipped out of adjustment. A
random sample of 64 caps is taken. If the mean diameter for this sample is 1.87
cm, does this indicate that the machine has slipped out of adjustment and needs
correction? Test at α = 0.01.
Procedure for Hypothesis Testing if σ is unknown
Same as for when σ is known except:
1. To find the critical region value (tc), stop at d.f. = _______, where n =
____________________.
2. Use ___________ in calc to find t-value. May require putting data into L1
Ex. 1 H.J. Heinz, Campbell Soup, Kellogg, Hershey Foods, Quaker Oats, and
so on are important food producers. How profitable are such food companies?
Let x be a random variable that represents annual profit as a percentage of
assets for the nation’s largest food companies. Assume that x has a distribution
that is approximately normal with mean μ = 6.6 %. Suppose that recent
financial reports for randomly selected national food companies gave the
following x values:
6.6
9.1
3.3
2.5
8.4
5.1
4.8
3.4
Use a 5% level of significance to test the claim that the population average
annual profits as a percentage of assets for large food companies has dropped.
Day 1 Assignment
P. 426 #1-4, 7, 8, 11, 13
Day 2 Assignment
P. 426 #5, 6, 9, 10, 17, 19, 20