SOLUTION: In a random sample of 80 workers from a factory in City A, it was found that 5% were unable to read, while in a random sample of 50 workers in city B, 8% were unable to read. Can

Question 1161977: In a random sample of 80 workers from a factory in City A, it was found that 5% were unable to read, while in a random sample of 50 workers in city B, 8% were unable to read. Can it be concluded that there is a difference in the proportions of nonreaders in the two cities? Use alpha = .10. Find the 90% confidence interval for the difference of the two proportions. Does the confidence interval support your original conclusion?
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The difference between two proportions test is
z=(p1-p2)/sqrt(p1(1-pi)/n1+p2(1-p2)/n2))
The half-interval of the CI is the z*SE, where z(0.95) =1.645 for a 90% CI
That is added to and subtracted from the difference of the means, which is -0.03 if we make it p(A)-p(B)
Ho:p(A)-p(B)=0
Ha: p(A)-p(B) does not equal 0
alpha=0.10 p{reject Ho|Ho true}
SE=sqrt (.05*.95/80+.08*.92/50)
=0.04545
the z value is -0.66, p-value=0.49 so Ho is not rejected
The half-interval is z*SE=1.645*0.0454=0.075
the interval is (-0.105, +0,.045). Because 0 is in the confidence interval, we are 90% confident that the true parameter of the difference is in the interval, and because 0 is in the interval, that is another way of saying the two proportions could be part of the same population and therefore not different,

RELATED QUESTIONS
"A random sample of 80 cell phones was inspected in a cell phone factory. It was found... (answered by stanbon)

A random sample of 1200 workers in a particular city found 348 workers who had donated... (answered by Boreal)

Given the following situation, how would you use Megastat to test whether the two... (answered by stanbon)

A random sample of 700 workers in a particular city found 168 workers who had donated to... (answered by Boreal)

State the null hypothesis and the alternative hypothesis in (a) words and in (b)... (answered by CPhill)

The human resource manager for a city is evaluating a program designed to improve the... (answered by CPhill)

A certain item is manufactured by 3 factories. Suppose we have a stockpile of the items... (answered by Boreal)

Factories A and B produce all of the computers sold at Cheapo Discount Stores. Factory A... (answered by Boreal)

The average score in the entrance examination in Mathematics at CBN High School is 80... (answered by rothauserc)