Question

For these questions, please use the “traditional method” that we covered in class (and appears on page 341 in the text). In a simple random sample of 70 automobiles registered in a certain state, 28 of them were found to have emission levels that exceed a state standard.

1.How many automobiles must be sampled to specify the proportion that exceed the standard to within ±0.10 with 95% confidence? Use your estimate from Question 1 for p. Round your answer up to the nearest whole number.

2.How many automobiles must be sampled to specify the proportion that exceed the standard to within ±0.10 with 98% confidence? Use your estimate from Question 1 for p. Round your answer up to the nearest whole number.

Answer 1

1)

here margin of error E =	0.100
for95% CI crtiical Z          =	1.960
estimated proportion=p=	0.400
required sample size n =	p*(1-p)*(z/E)2=	93.00

2)

here margin of error E =	0.100
for98% CI crtiical Z          =	2.33
estimated proportion=p=	0.400
required sample size n =	p*(1-p)*(z/E)2=	131.00

(try 130 if z value is not rounded to 2 places)