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CHAPTER 10B 8 CENGAGE 02021 Cergage Leaming. Ad Rights Reserved. May not be scanred, copied of dupicated, of posted to a putely accessible websile, in whole or in part. Interval Estimation of \( \boldsymbol{p}_{\mathbf{1}}-\boldsymbol{p}_{\mathbf{2}} \) (3 of 5) Example: Tax preparation firm Independent random samples from the two offices provide the following information: Office 1 \( n_{1}=250 \) Number of returns with errors \( =35 \) Office 2 \( n_{2}=300 \) Number of returns with errors \( =27 \) CENGAGE © 2021 Cengage teaming. Ad Righte Reserved. May not be scanned, copied of duplicated, or pouted to a publicy accousible wibsias, in whole or in part. Point Estimator of the Difference between Two Population Proportions Example: Tax preparation firm \( p_{1}= \) proportion of erroneous returns for population 1 (office 1) \( p_{2}= \) proportion of erroneous returns for population 2 (office 2) \( \bar{p}_{1}= \) sample proportion for a random sample from population 1 \( \bar{p}_{2}= \) sample proportion for a random sample from population 2 \[ \bar{p}_{1}-\bar{p}_{2}=\frac{35}{250}-\frac{27}{300}=.14-.09=.05 \] CENGAGE © 2021 Cergage Learning. Ad Rights Reserved. May not be scanned, copied or duplicated, or posted lo a publichy accessible wobsise, in whole or in part. Interval Estimation of \( p_{1}-p_{2} \) (4 of 5)

          CHAPTER 10B

8
CENGAGE
02021 Cergage Leaming. Ad Rights Reserved. May not be scanred, copied of dupicated, of posted to a putely accessible websile, in whole or in part.

Interval Estimation of \( \boldsymbol{p}_{\mathbf{1}}-\boldsymbol{p}_{\mathbf{2}} \) (3 of 5)

Example: Tax preparation firm
Independent random samples from the two offices provide the following information:

Office 1
\( n_{1}=250 \)
Number of returns with errors \( =35 \)

Office 2
\( n_{2}=300 \)
Number of returns with errors \( =27 \)
CENGAGE
© 2021 Cengage teaming. Ad Righte Reserved. May not be scanned, copied of duplicated, or pouted to a publicy accousible wibsias, in whole or in part.

Point Estimator of the Difference between Two Population Proportions

Example: Tax preparation firm
\( p_{1}= \) proportion of erroneous returns for population 1 (office 1)
\( p_{2}= \) proportion of erroneous returns for population 2 (office 2)
\( \bar{p}_{1}= \) sample proportion for a random sample from population 1
\( \bar{p}_{2}= \) sample proportion for a random sample from population 2
\[
\bar{p}_{1}-\bar{p}_{2}=\frac{35}{250}-\frac{27}{300}=.14-.09=.05
\]
CENGAGE
© 2021 Cergage Learning. Ad Rights Reserved. May not be scanned, copied or duplicated, or posted lo a publichy accessible wobsise, in whole or in part.
Interval Estimation of \( p_{1}-p_{2} \) (4 of 5)

CHAPTER 10B

8
CENGAGE
02021 Cergage Leaming. Ad Rights Reserved. May not be scanred, copied of dupicated, of posted to a putely accessible websile, in whole or in part.

Interval Estimation of p1-p2 (3 of 5)

Example: Tax preparation firm
Independent random samples from the two offices provide the following information:

Office 1
n1=250
Number of returns with errors =35

Office 2
n2=300
Number of returns with errors =27
CENGAGE
© 2021 Cengage teaming. Ad Righte Reserved. May not be scanned, copied of duplicated, or pouted to a publicy accousible wibsias, in whole or in part.

Point Estimator of the Difference between Two Population Proportions

Example: Tax preparation firm
p1= proportion of erroneous returns for population 1 (office 1)
p2= proportion of erroneous returns for population 2 (office 2)
p̅1= sample proportion for a random sample from population 1
p̅2= sample proportion for a random sample from population 2

p̅1-p̅2=(35)/(250)-(27)/(300)=.14-.09=.05

CENGAGE
© 2021 Cergage Learning. Ad Rights Reserved. May not be scanned, copied or duplicated, or posted lo a publichy accessible wobsise, in whole or in part.
Interval Estimation of p1-p2 (4 of 5)

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