og Do Hemwork-Haylee Floyd-Google Choome Essentials of Statistics MATH 2843 001R
ID: 3364243 • Letter: O
Question
og Do Hemwork-Haylee Floyd-Google Choome Essentials of Statistics MATH 2843 001R Online F 2017 Homework: Homework Score: 0 of 1 pt 7.3.35 11 Save 190120 (12 complete) HW Score: 54.71%, 10.94 of 20 pts Quest on Help * Using the simple random sample of weights of women from a data set, we ottain these sample statistics n 50 and x -1 sources suggests that the tation of weghts of wone has a standard devir ongven by-32 42 p a, Find the best point estimate of the mean weght of al women t. Find a 95% conhdence interval estmate of the mean we gntot at wornen cickher a. The best point estimate is 14051 I Type an integer or a decimal ) b.The 95% conndence mervai estam ate stExplanation / Answer
TRADITIONAL METHOD
given that,
standard deviation, =32.42
sample mean, x =140.51
population size (n)=50
I.
stanadard error = sd/ sqrt(n)
where,
sd = population standard deviation
n = population size
stanadard error = ( 32.42/ sqrt ( 50) )
= 4.585
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
value of z table is 1.96
margin of error = 1.96 * 4.585
= 8.986
III.
CI = x ± margin of error
confidence interval = [ 140.51 ± 8.986 ]
= [ 131.52,149.50]
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DIRECT METHOD
given that,
standard deviation, =32.42
sample mean, x =140.51
population size (n)=50
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
value of z table is 1.96
we use CI = x ± Z a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
Za/2 = Z-table value
CI = confidence interval
confidence interval = [ 140.51 ± Z a/2 ( 32.42/ Sqrt ( 50) ) ]
= [ 140.51 - 1.96 * (4.585) , 140.51 + 1.96 * (4.585) ]
= [ 131.52,149.50]
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interpretations:
1. we are 95% sure that the interval [131.524 , 149.496 ] contains the true population mean
2. if a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population mean
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