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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, alpha = 0.01, n = 13
2.
Right tailed test, alpha = 0.10, n =10
3.
Two tailed test, alpha = 0.05, n = 22
Guidelines for the t-Test
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find H0 and Ha
Identify the level of significance, alpha
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, alpha = 0.05,
sample mean = 26.2, s = 2.32, n = 17
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15. Claim: µ > 8000, alpha = 0.01,
sample mean = 7700, s = 450, n = 25
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20. 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?
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26. 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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1. find H0 and Ha
2. identify alpha
3. find the critical value(s)
4. shade the rejection region(s)
5. find 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.

4. Claim: p > 0.48, alpha = 0.08,
sample proportion = 0.40, n = 90
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8. Claim: p = 0.95, alpha = 0.10,
sample proportion = 0.875, n = 50
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14. 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 alpha = 0.05, is there
enough evidence to reject the
researcher’s claim?
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16. A humane society claims that
30% of US households own a cat. In
a random sample of 200 US
households, 72 say they own a cat.
At alpha = 0.05, is there enough
evidence to reject the society’s
claim?