Question

A recent study of two vendors of desktop personal computers reported that out of 895 units sold by Brand A, 102 required repair, while out of 788 units sold by Brand B, 96 required repair. Round all numeric answers to 4 decimal places.

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

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

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

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

A. Yes
B. No

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. little evidence
B. very strong evidence
C. some evidence
D. strong evidence
E. extremely strong evidence
that the null model is not a good fit for our observed data.

8. Compute a 95 % confidence interval for the difference ?̂??????−?̂??????p^BrandA−p^BrandB = (   ,  )

Answer 1

1)

	A		B
x1                =	102	x2                =	96
p̂1=x1/n1 =	0.1140	p̂2=x2/n2 =	0.1218
n1                       =	895	n2                       =	788
estimated prop. diff =p̂1-p̂2    =		-0.0079

2)

A. ?0:??−??=0H0:pA−pB=0, ??:??−??≠0HA:pA−pB≠0

3)

pooled prop p̂ =(x1+x2)/(n1+n2)=

0.1176

4)

yes

5)

std error Se=√(p̂1*(1-p̂1)*(1/n1+1/n2) =

0.0157

test stat z=(p̂1-p̂2)/Se =

-0.4995

6)

P value   =

0.6175

7) A. little evidence

8)

std error Se =√(p̂1*(1-p̂1)/n1+p̂2*(1-p̂2)/n2) =			0.0158
for 95 % CI value of z=		1.960
margin of error E=z*std error =		0.0309
lower bound=(p̂1-p̂2)-E=		-0.0388
Upper bound=(p̂1-p̂2)+E=		0.0230
from above 95% confidence interval for difference in population proportion =(-0.0388 , 0.0230)