Question 15 6 out of 8 points The inspection division of the Chattanooga CoCa-Co

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Question 15 6 out of 8 points The inspection division of the Chattanooga CoCa-Cola Bottling Company is interested in estimating the actual amount of soft drink that is placed in 2-liter bottles. The bottling plant has informed the inspection division that the standard deviation for 2-liter bottles is 0.05 liter based on history data of many years (analogue to population standard deviation a). A random sample of 100 2-liter bottles obtained from the plant indicates a sample mean of 1.98 liters. Set up a 95% confidence interval estimate of the true population mean amount soft drink reach bottle. (1) You use [a] (fill in the blank by z or t) distribution to obtain the critical value (2) The absolute critical value [D] (3) The lower limit of the CI-C] (4DP), the upper limit of the C/ =[d] ADP) Specified Answer for: a z Specified Answer for: b 1.960 Specified Answer for: c 1.9702 Specified Answer for: d 1.9898

Explanation / Answer

15.

TRADITIONAL METHOD
given that,
standard deviation, =0.05
sample mean, x =1.98
population size (n)=100
I.
stanadard error = sd/ sqrt(n)
where,
sd = population standard deviation
n = population size
stanadard error = ( 0.05/ sqrt ( 100) )
= 0.005
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 * 0.005
= 0.01
III.
CI = x ± margin of error
confidence interval = [ 1.98 ± 0.01 ]
= [ 1.97,1.99 ]
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DIRECT METHOD
given that,
standard deviation, =0.05
sample mean, x =1.98
population size (n)=100
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 = [ 1.98 ± Z a/2 ( 0.05/ Sqrt ( 100) ) ]
= [ 1.98 - 1.96 * (0.005) , 1.98 + 1.96 * (0.005) ]
= [ 1.97,1.99 ]
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interpretations:
1. we are 95% sure that the interval [1.97 , 1.99 ] 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
[ANSWERS]
best point of estimate = mean = 1.98
standard error =0.005
z table value = 1.96
margin of error = 0.01
confidence interval = [ 1.97 , 1.99 ]

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