14 Now keep the error probability at = 0.05. We want to build an interval which
ID: 3047769 • Letter: 1
Question
14 Now keep the error probability at = 0.05. We want to build an interval which captures 95% of the sample means within ±4 from the population mean. What is the minimum sample size that would yield such an interval?
a 601
b 583
c 542
d 507
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A recent article in a business journal reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation is 4 weeks.
15 What is the probability that a random sample of 50 unemployed persons will provide a sample mean within 1 week of the population mean?
a 0.9476
b 0.9232
c 0.8882
d 0.8414
16 What fraction of the sample means fall within ±1 standard error from the population mean?
a 0.6826
b 0.7698
c 0.8384
d 0.9198
Explanation / Answer
15)
mean = 17.5, s = 4 , n = 50
we need to find P( ( 17.5 - 1) < x < ( 17.5 + 1))
p(16.5 < x < 18.5)
By central limit theorem,
z = P((16.5 - 17.5) / (4/sqrt(50)) < z < ((18.5 - 17.5) / (4/sqrt(50))
= P(-1.767 < x < 1.767)
we need to find P((-1.767 < z < 1.767) by using z standard right tail, we get,
P(16.5 < x < 18.5) = P((-1.767 < z < 1.767)
= 0.9232
16)
By empirical rule, 68% of data fall within ±1 standard error from the population mean
answer is a) 0.6826
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