Question

Question 5 options:

Poor millennials ~ Skyrocketing cost of living and crippling student debt have made it much more difficult for millennials to accumulate wealth. A random sample of 60 baby boomer households and a random sample of 76 millennial households were selected. The summary statistics are given in the table below in thousands of dollars. Population/Group Generation Mean Household wealth Standard Deviation 1 Baby Boomers 1.0510 0.027 2 Millennials 0.1197 0.020 Kanye, an economics student, wants to estimate the difference between the actual mean household wealth of baby boomers and millennials. Note: Numbers are randomized in each instance of this question. Pay attention to the numbers given above. What is the upper bound for a 90% confidence interval for the difference between the population means? Your Answer:

Answer 1

5.

TRADITIONAL METHOD
given that,
mean(x)=1.051
standard deviation , s.d1=0.027
number(n1)=60
y(mean)=0.1197
standard deviation, s.d2 =0.02
number(n2)=76
I.
standard error = sqrt(s.d1^2/n1)+(s.d2^2/n2)
where,
sd1, sd2 = standard deviation of both
n1, n2 = sample size
standard error = sqrt((0.001/60)+(0/76))
= 0.004
II.
margin of error = t a/2 * (standard error)
where,
t a/2 = t -table value
level of significance, α = 0.1
from standard normal table, two tailed and
value of |t α| with min (n1-1, n2-1) i.e 59 d.f is 1.671
margin of error = 1.671 * 0.004
= 0.007
III.
CI = (x1-x2) ± margin of error
confidence interval = [ (1.051-0.1197) ± 0.007 ]
= [0.924 , 0.938]
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DIRECT METHOD
given that,
mean(x)=1.051
standard deviation , s.d1=0.027
sample size, n1=60
y(mean)=0.1197
standard deviation, s.d2 =0.02
sample size,n2 =76
CI = x1 - x2 ± t a/2 * Sqrt ( sd1 ^2 / n1 + sd2 ^2 /n2 )
where,
x1,x2 = mean of populations
sd1,sd2 = standard deviations
n1,n2 = size of both
a = 1 - (confidence Level/100)
ta/2 = t-table value
CI = confidence interval
CI = [( 1.051-0.1197) ± t a/2 * sqrt((0.001/60)+(0/76)]
= [ (0.931) ± t a/2 * 0.004]
= [0.924 , 0.938]
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interpretations:
1. we are 90% sure that the interval [0.924 , 0.938] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
Answer:
the upper bound for a 90% confidence interval for the difference between the population means is 0.938