SOLUTION: A smartphone company is interested in comparing the quality of work at two of its factories. By randomly selecting samples of smartphones manufactured at each factory and testing t

Question 1174838: A smartphone company is interested in comparing the quality of work at two of its factories. By randomly selecting samples of smartphones manufactured at each factory and testing their reliability, the company will be able to estimate the proportion of malfunctioning smartphones manufactured at each factory. Of particular interest is the difference between these proportions. Independent simple random samples from the two offices provide the following information:
Factory 1
Factory 2
n1 = 250
n2 = 300
Number of malfunctioning phones = 35
Number of malfunctioning phones = 27

a. What is the point estimate of the difference between the two population proportions (p1 - p2)? 2pts
b. Develop a 95% confidence interval for the difference between the two population proportions (p1 - p2). 7pts
c. Develop a 90% confidence interval for the difference between the two population proportions (p1 - p2). 7pts
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
p1=35/250=0.14
p2=27/300=0.09
p1-p2 point estimate is 0.05
std error is sqrt { (p hat*(1- phat)* (1/n1)+(1/n2)} p hat is pooled proportion or 62/550=0.1127
=sqrt ((p1*(1-p1)/n1+p2(1-p2)/n2))=sqrt(0.14*0.86/250+0.09*0.91/300)=0.0275
multiply that by 1.96 to get the half-interval of the difference at the 95% level=0.0538
CI=(-0.0038, 0.1038)
for 90%, use 1.645 and get a half-interval of 0.0452
CI=(0.0048, 0.0952)
Notice the first contains 0, so the p-value is between 0.05 and 0.10

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