Question

A recent study of two vendors of desktop personal computers reported that out of 858 units sold by Brand A, 126 required repair, while out of 779 units sold by Brand B, 97 required repair. Round all numeric answers to 4 decimal places.

1. Calculate the difference in the sample proportion for the two brands of computers, ?̂ ??????−?̂ ?????? = .

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands.

A. ?0:??−??=0, ??:??−??<0 B. ?0:??−??=0, ??:??−??>0 C. ?0:??−??=0, ??:??−??≠0

3. Calculate the pooled estimate of the sample proportion, ?̂ =

4. Is the success-failure condition met for this scenario? A. Yes B. No

5. Calculate the test statistic for this hypothesis test. =

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

7. Based on the p-value, we have:

A. very strong evidence

B. extremely strong evidence

C. strong evidence

D. little evidence

E. some evidence that the null model is not a good fit for our observed data.

8. Compute a 90 % confidence interval for the difference ?̂ ??????−?̂ ?????? = ( , )

Answer 1

1)

	Brand A		Brand B
x1                =	126	x2                =	97
p̂1=x1/n1 =	0.1469	p̂2=x2/n2 =	0.1245
n1                       =	858	n2                       =	779
estimated prop. diff =p̂1-p̂2    =		0.0223

?̂ ??????−?̂ ?????? = 0.0223

2)

C. ?0:??−??=0, ??:??−??≠0

3)

pooled prop p̂ =(x1+x2)/(n1+n2)=

0.1362

4)

Yes

5)

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =		0.0170
test stat z=(p̂1-p̂2)/Se =		1.3156

6_)

P value   =

0.1883

7)

D. little evidence

8)

estimated difference in proportion   =p̂1-p̂2   =			0.0223
std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0169
for 90 % CI value of z=		1.645
margin of error E=z*std error =		0.0278
lower bound=(p̂1-p̂2)-E=		-0.0055
Upper bound=(p̂1-p̂2)+E=		0.0501
from above 90% confidence interval for difference in population proportion =(-0.0055 , 0.0501)