Question

(1 point) A random sample of n measurements was selected from a population with unknown mean u and standard deviation o. Calculate a 90% confidence interval for u for each of the following situations: (a) n= m = 100, 7 100, = 102.2, s = 2.28 su < 101.825 102.575 (b) n = 90, z = 84.8, s = = 2.19 184.420 su < 185.180 (c) n 80, # 55.8, s = 2.48 su < 55.3444 56.2561 (d) n = 90, ã = 76.3, s = 2.68 75.835 su < 76.765

just got b wrong

Answer 1

The formula for estimation is:

μ = M ± t(s_M)

where:

M = sample mean
t = t statistic determined by confidence level
s_M = standard error = √(s²/n)

a)

sample mean (x^-) : 102.2

sample size (n) : 100

standard deviation(s) : 2.28

Calculation

x^- = 102.2
t = 1.66
s_M = √(2.28²/100) = 0.23

μ = x^-± t*(s_M)
μ = 102.2 ± 1.66*0.23
μ = 102.2 ± 0.379

90% CI [101.821, 102.579].

b)

sample mean (x^-) : 84.8

sample size (n) : 90

standard deviation(s) : 2.19

Calculation

x^- = 84.8
t = 1.66
s_M = √(2.19²/90) = 0.23

μ = x^- ± t*(s_M)
μ = 84.8 ± 1.66*0.23
μ = 84.8 ± 0.384

= [84.416, 85.184].

90% CI [84.416, 85.184].

c)

sample mean (x^-) : 55.8

sample size (n) : 80

standard deviation(s) : 2.48

Calculation

x^- = 55.8
t = 1.66
s_M = √(2.48²/80) = 0.28

μ = x^- ± t*(s_M)
μ = 55.8 ± 1.66*0.28

=  [55.339, 56.261]

90% CI [55.339, 56.261].

d)

sample mean (x^-) : 76.3

sample size (n) : 90

standard deviation(s) : 2.68

Calculation

x^- = 76.3
t = 1.66
s_M = √(2.68²/90) = 0.28

μ = x^- ± t * (s_M)
μ = 76.3 ± 1.66*0.28
μ = 76.3 ± 0.47
μ = 55.8 ± 0.46

=  [75.83, 76.77].

90% CI [75.83, 76.77].

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