Calculate a confidence interval for each data set, using 95% confidence, the sam

Question

Calculate a confidence interval for each data set, using 95% confidence, the sample size, and the standard error you calculate using the formula. Make sure the imerval is shown in the proper forma. Follow the format given below: Year Raw Data 6.3 8.5 8.8 8.1 7.3 2010 2013 2016 2017 Data Set Name Insert Values Below Standard 2 tvalue 3 Interval Estimate Meanc Raw Data 2008 11.2 13.7 10.9 2010 2011 2012 2013 2014 7.9 2016 2017 Data Set Name Insert Values Below Standard 2 tvalue 3 Interval Estimate Meanc

Explanation / Answer

PART A.
given that,
sample mean, x =5.7455
standard deviation, s =2.1929
sample size, n =11
I.
stanadard error = sd/ sqrt(n)
where,
sd = standard deviation
n = sample size
standard error = ( 2.1929/ sqrt ( 11) )
= 0.661
II.
ta/2 = t-table value
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 10 d.f is 2.228
III.
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 10 d.f is 2.228
we use CI = x ± t a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 5.7455 ± t a/2 ( 2.1929/ Sqrt ( 11) ]
= [ 5.7455-(2.228 * 0.661) , 5.7455+(2.228 * 0.661) ]
= [ 4.272 , 7.219 ]

PART B.
given that,
sample mean, x =8.4
standard deviation, s =2.7232
sample size, n =11
I.
stanadard error = sd/ sqrt(n)
where,
sd = standard deviation
n = sample size
standard error = ( 2.7232/ sqrt ( 11) )
= 0.821
II.
ta/2 = t-table value
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 10 d.f is 2.228.
III.
level of significance, = 0.05
from standard normal table, two tailed value of |t /2| with n-1 = 10 d.f is 2.228
we use CI = x ± t a/2 * (sd/ Sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 8.4 ± t a/2 ( 2.7232/ Sqrt ( 11) ]
= [ 8.4-(2.228 * 0.821) , 8.4+(2.228 * 0.821) ]
= [ 6.571 , 10.229 ]

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