Comparing one proportion to a number

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Comparing one proportion to a number Comparing
two proportions to each other
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1. 2. Zobs N(0,1) if H0 is true 3. za (left
tailed) z1-a (right tailed) za/2, z1-a/2 (two
tailed) 4. Reject H0 if Zobs lt za Reject H0
if Zobs gt z1-a Reject H0 if Zobs lt za/2 or
Zobs gt z1-a/2 5. 6. Reject H0 OR Fail to
reject H0 7. Conclusion
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1. 2. Zobs N(0,1) if H0 is true 3. Reject if
p-value lt a 4. 5. P(Z lt Zobs) (left tailed)
P(Z gt Zobs) (right tailed) P(Z lt -Zobs
or Z gt Zobs) (two tailed) 6. Reject H0 OR
Fail to reject H0 7. Conclusion
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Confidence interval
Sample size with specified confidence and margin
of error
ALWAYS ROUND UP
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In a random sample of 130 preschool age children,
it was found that 72 regularly watch Barney.
Research in the previous year found that 52 were
regular viewers. Has this proportion
significantly increased using a 0.05 type I error
rate?
x 72 n 130 p0 0.52 a 0.05
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1. H0 p 0.52, H1 p gt 0.52 2. Zobs N(0,1) if
H0 is true 3. z0.95 1.64 4. Reject H0 if Zobsgt
1.64 5. 6. Fail to reject H0 7. With 95
confidence there is insufficient evidence that
more than 52 of pre-school age children watch
Barney.
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1. H0 p 0.52, H1 p gt 0.52 2. Zobs N(0,1) if
H0 is true 3. Reject if p-value lt 0.05 4. 5.
P(Z gt 0.77) 0.2206 6. Fail to reject H0 7. With
95 confidence there is insufficient evidence
that more than 52 of pre-school age children
watch Barney.
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With 95 confidence, between 46.84 and 63.93 of
pre-school age children watch Barney.
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How many people need to be surveyed in order to
be within 4 of the true proportion with 90
confidence?
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0. Name populations 1. H0 p1 p2 0, H1 p1
p2 0 2. Zobs N(0,1) if H0 is true 3. za
(left tailed) z1-a (right tailed) za/2, z1-a/2
(two tailed) 4. Reject H0 if Zobs lt za Reject
H0 if Zobs gt z1-a Reject H0 if Zobs lt za/2 or
Zobs gt z1-a/2 5. 6. Reject H0 OR Fail to
reject H0 7. Conclusion
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0. Name populations 1. H0 p1 p2 0, H1 p1
p2 0 2. Zobs N(0,1) if H0 is true 3. Reject
if p-value lt a 4. 5. P(Z lt Zobs) (left
tailed) P(Z gt Zobs) (right tailed) P(Z lt
-Zobs or Z gt Zobs) (two tailed) 6. Reject
H0 OR Fail to reject H0 7. Conclusion
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Confidence interval
Sample size with specified confidence and margin
of error
ALWAYS ROUND UP
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In a recent survey, it was found that 79 of 797
men were unemployed and 88 of 732 women were
unemployed. At the 0.05 level of significance,
are the unemployment rates for males and females
different?
Pop1 Men Pop 2 Women x1 79 x2 88 n1
797 n2 732 a 0.05 Test for a
difference between p1 and p2
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0. pop1men, pop2women 1. H0 p1 p2 0, H1
p1 p2 ? 0 2. Zobs N(0,1) if H0 is true 3.
z0.025 -1.96, z0.975 1.96 4. Reject H0 if
Zobs lt -1.96 or Zobs gt 1.96 5. 6. Fail to
reject H0 7. With 95 confidence there is
insufficient evidence that the unemployment rates
are different between men and women.
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0. pop1men, pop2women 1. H0 p1 p2 0, H1
p1 p2 ? 0 2. Zobs N(0,1) if H0 is true 3.
z0.025 -1.96, z0.975 1.96 4. 5.
P(Zlt-1.32 or Zgt1.32) 0.1868 6. Fail to reject
H0 7. With 95 confidence there is insufficient
evidence that the unemployment rates are
different between men and women.
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Confidence interval
With 95 confidence the difference in
unemployment rates between men and women is
between -0.0544 and 0.0122.
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How many people need to be surveyed in order to
be within 3 of the true difference between two
proportions with 95 confidence?