Question

1 point) A package delivery service wants to compare the proportion of on-time deliveries for two of its major service areas. In City A, 366 out of a random sample of 431 deliveries were on time. A random sample of 273 deliveries in City B showed that 216 were on time.

1. Calculate the difference in the sample proportion for the delivery times in the two cities.

?̂ ?????−?̂ ?????p^CityA−p^CityB =

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of deliveries that are on time in City A is different from than the proportion in City B?

A. ?0:??=??H0:pA=pB, ??:??>??HA:pA>pB
B. ?0:??=??H0:pA=pB, ??:??≠??HA:pA≠pB
C. ?0:??=??H0:pA=pB, ??:??<??HA:pA<pB

3. Calculate the pooled estimate of the sample proportion.

?̂ p^ =

4. Is the success-failure condition met for this scenario?

A. No
B. Yes

5. Calculate the test statistic for this hypothesis test.

? z t X^2 F  =

6. Calculate the p-value for this hypothesis test.

p-value =

7. Based on the p-value, we have:
A. some evidence
B. very strong evidence
C. little evidence
D. strong evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

8. Compute a 90% confidence interval for the difference ?̂ ?????−?̂ ?????p^CityA−p^CityB.

( , )

Answer 1

1)

x1                =	366	x2                =	216
p̂1=x1/n1 =	0.8492	p̂2=x2/n2 =	0.7912
n1                       =	431	n2                       =	273
estimated prop. diff =p̂1-p̂2    =		0.0580

2)

option B is correct

3)

pooled prop p̂ =(x1+x2)/(n1+n2)=

0.8267

4)B. Yes

5)

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0293
test stat z=(p̂1-p̂2)/Se =		1.9803

6)

P value   =

0.0477

7)

D. strong evidence

8_)

estimated difference in proportion   =p̂1-p̂2   =			0.0580
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0300
for 90 % CI value of z=		1.645
margin of error E=z*std error =		0.0494
lower bound=(p̂1-p̂2)-E=		0.0086
Upper bound=(p̂1-p̂2)+E=		0.1074
from above 90% confidence interval for difference in population proportion =(0.0086 ,0.1074)