MATH 1410/8.1 and 8.2 pp.ppt
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Transcript MATH 1410/8.1 and 8.2 pp.ppt
Hypothesis Testing
with TWO Samples
Section 8.1
2 samples are independent if the sample
selected from one population is not related
to the sample selected from the 2nd
population.
2 samples are dependent if each member of
one sample corresponds to a member of
the other sample. (a.k.a. Paired or
Matched samples)
Sample 1: the SAT scores of 44 high school
students.
Sample 2: the SAT scores of the same 44
high school students after taking an SAT
preparation course.
Sample 1: the IQ scores of 60 females
Sample 2: The IQ scores of 60 males
3 ways the NULL hypothesis can be written:
µ1 = µ2
µ1 < µ2
µ1 > µ2
The samples must be randomly selected,
independent, and each sample size must
be at least 30
If n is not > 30, then each population must
have a normal distribution with σ
known.
1.
2.
3.
4.
5.
6.
7.
State the hypotheses
Specify level of significance, α
Determine the critical value(s)
Shade the rejection region(s)
Find the test statistic, z (new formula)
Make decision to reject or not reject H0
Interpret the decision in context
16.
To compare the amounts spent in the
first three months by clients of two mealreplacement diets, a researcher randomly
selects 20 clients of each diet. The mean
amount spent for Diet A is $643. Assume
the population standard deviation is $89.
The mean amount spent for Diet B is $588.
Assume the population standard deviation
is $75. At α = 0.01, can the researcher
support the claim that the mean amount
spent in the first three months by clients of
Diet A is greater than the mean amount
spent in the first three months of Diet B?
Section 8.2
14. A magazine claims that the mean amount
spent by a customer at Burger World is greater
than the mean amount spent by a customer at
Fry World. The results for samples of
customer transactions for the 2 fast food
restaurants are shown below. At α = 0.05, can
you support the magazine’s claim? Assume the
population variances are equal.
Burger Stop
Fry World
s1 = $0.89
s2 = $0.79
n1 = 22
n2 = 30