Transcript MATH 1410/7.3 and 7.4 pp

Section 7.3
Hypothesis Testing for the
Mean (Small Samples)
Similar to section 7.2…
When the distribution is normal (or
nearly normal), n < 30 or σ is
unknown.
 Use the t-distribution table:
 Degrees of freedom: d.f. = n – 1
EX: find critical value, t0
1.
Left tailed test, α = 0.01, n = 13
2.
Right tailed test, α = 0.10, n =10
3.
Two tailed test, α = 0.05, n = 22
Guidelines for the t-Test
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find H0 and Ha
Identify the level of significance, α
Identify the degrees of freedom, d.f.
Find the critical value(s) using the table.
Sketch the curve and shade the rejection
region(s)
Find t
Make the decision to reject or not reject
H0
Interpret the decision in context.
Use a t-test to test the claim
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14. Claim: µ > 25, α = 0.05, sample
mean = 26.2, s = 2.32, n = 17
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15. Claim: µ > 8000, α = 0.01,
sample mean = 7700, s = 450, n = 25
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18. A company claims that the mean
battery life of their MP3 player is at
least 30 hours. You suspect that the
claim is incorrect and find that a
random sample of 18 MP3 players has
a mean battery life of 28.5 hours and
a standard deviation of 1.7 hours. Is
there enough evidence to reject the
claim at alpha = 0.01?

A repair shop believes that people
travel more than 3500 miles
between oil changes. A random
sample of 8 cars getting an oil
change has a mean distance of 3375
miles since the last oil change with a
standard deviation of 225 miles. At
alpha = 0.05, do you have enough
evidence to support the shop’s
claim?
Section 7.4
HYPOTHESIS
TESTING FOR
PROPORTIONS
Uses the z-Test
Guidelines for the z-Test
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np and nq both must be at least 5
1. find H0 and Ha
2. identify α
3. find the critical value(s)
4. shade the rejection region(s)
5. calculate z
6. make decision to reject or not
reject the null hypothesis
7. interpret decision in context
Determine if a normal
distribution can be used. If so,
test the claim.
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A research center claims that 16% of
US adults say that curling is the
Winter Olympic sport they would like
to try the most. In a random sample
of 300 US adults, 20% say that curling
is the Winter Olympic sport they
would like to try the most. At α =
0.05, is there enough evidence to
reject the researcher’s claim?
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A research center claims that at
most 75% of US adults think that
drivers are safer using hands-free
cell phones instead of using handheld cell phones. In a random
sample of 150 US adults, 77% think
that drivers are safer using handsfree cell phones instead of handheld cell phones. At α = 0.01, is
there enough evidence to reject the
center’s claim?