Question

1) Find the critical value t (a/2) needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places

a) 98% sample size 11

critical value-

b) for level 95% and sample size 25

critical value-

c)for level 99% and sample size 14

2) a sample of size n equals 45 has a sample mean X equals 56.9 and sample standard deviation s equals 9.4.

construct a 99% confidence interval for the population mean U. Round the answer to one decimal place

A 99% confidence interval for the population mean is ____ < U < _____

Answer #1

1)

a)

sample size, n = 11

degrees of freedom, df = n - 1 = 10

Given CI level is 98%, hence α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.764

b)

sample size, n = 25

degrees of freedom, df = n - 1 = 24

Given CI level is 95%, hence α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.064

c)

sample size, n = 14

degrees of freedom, df = n - 1 = 13

Given CI level is 99%, hence α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.012

2)

sample mean, xbar = 56.9

sample standard deviation, s = 9.4

sample size, n = 45

degrees of freedom, df = n - 1 = 44

Given CI level is 99%, hence α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 2.692

ME = tc * s/sqrt(n)

ME = 2.692 * 9.4/sqrt(45)

ME = 3.772

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))

CI = (56.9 - 2.692 * 9.4/sqrt(45) , 56.9 + 2.692 *
9.4/sqrt(45))

CI = (53.1 , 60.7)

Find the critical value
t/α2
needed to construct a confidence interval of the given level
with the given sample size. Round the answers to three decimal
places.
Part 1 of 4
(a) For level
99%
and sample size
5
Part 2 of 4
(b) For level
90%
and sample size
14
Part 3 of 4
(c) For level
99.5%
and sample size
28
Part 4 of 4
(d) For level
95%
and sample size
11

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2.
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