Figure the standard deviation of the distribution of means for a population with
ID: 3022800 • Letter: F
Question
Figure the standard deviation of the distribution of means for a population witha, standard deviation of 20 and sample sizes of (a) 10. (b) 11, (c) 100. and (d) 10] ADVANCED TOPIC: Figure the 95% confidence interval (that is, the lower and upper confidence limits) for each part of problem 13. Assume that in each case the researcher's sample has a mean of 80 and the population of individuals is known to follow a normal curve. ADVANCED TOPIC. Figure the 99% confidence interval (that is, the loner - and upper confidence limits) for each part of problem 14. Assume that in each case the researcher's sample has a mean of 50 and that the population of individuals is known to follow' a normal curve.Explanation / Answer
16.
a)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 50
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 20
n = sample size = 10
Thus,
Margin of Error E = 16.29097493
Lower bound = 33.70902507
Upper bound = 66.29097493
Thus, the confidence interval is
( 33.70902507 , 66.29097493 ) [ANSWER]
*****************
b)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 50
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 20
n = sample size = 11
Thus,
Margin of Error E = 15.53283513
Lower bound = 34.46716487
Upper bound = 65.53283513
Thus, the confidence interval is
( 34.46716487 , 65.53283513 ) [ANSWER]
********************
c)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 50
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 20
n = sample size = 100
Thus,
Margin of Error E = 5.151658607
Lower bound = 44.84834139
Upper bound = 55.15165861
Thus, the confidence interval is
( 44.84834139 , 55.15165861 ) [ANSWER]
********************
d)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.005
X = sample mean = 50
z(alpha/2) = critical z for the confidence interval = 2.575829304
s = sample standard deviation = 20
n = sample size = 101
Thus,
Margin of Error E = 5.126091905
Lower bound = 44.87390809
Upper bound = 55.12609191
Thus, the confidence interval is
( 44.87390809 , 55.12609191 ) [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.