Question

A recent study of two vendors of desktop personal computers reported that out of 879 units sold by Brand A, 116 required repair, while out of 749 units sold by Brand B, 127 required repair. Round all numeric answers to 4 decimal places. 1. Calculate the difference in the sample proportion for the two brands of computers, ?̂??????−?̂??????= 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. little evidence B. some evidence C. extremely strong evidence D. strong evidence E. very 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^BrandA−p^BrandB= ( , )

Answer 1

Answer:

A recent study of two vendors of desktop personal computers reported that out of 879 units sold by Brand A, 116 required repair, while out of 749 units sold by Brand B, 127 required repair. Round all numeric answers to 4 decimal places.

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

=116/879 – 127/749

=0.1320-0.1696 = -0.0376

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

= (116+127)/(879+749) =0.1493

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

A. Yes

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

= -2.1214

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

p-value =0.0339 .

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

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

Note: at 5% and 10% level of significance, there is significant difference between the two brands. Interpret appropriately. At 1% level is not significant. Based on class notes, make your option.

8. Compute a 90 % confidence interval for the difference ?̂??????−?̂?????? p^BrandA−p^BrandB

= (-0.0669, -0.0082 )

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.05
Group 1
Number of Items of Interest	116
Sample Size	879
Group 2
Number of Items of Interest	127
Sample Size	749
Intermediate Calculations
Group 1 Proportion	0.1320
Group 2 Proportion	0.1696
Difference in Two Proportions	-0.0376
Average Proportion	0.1493
Z Test Statistic	-2.1214
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0339
Reject the null hypothesis

CI = p1-p2 ± z*se

Standard error of p1-p2= se=

Confidence Interval Estimate
of the Difference Between Two Proportions
Data
Confidence Level	90%
Intermediate Calculations
Z Value	1.645
Std. Error of the Diff. between two Proportions	0.0178
Interval Half Width	0.0293
Confidence Interval
Interval Lower Limit	-0.0669
Interval Upper Limit	-0.0082