Transcript MATH 1410/8.1 and 8.2 pp

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
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 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
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
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