Data has been analyzed from a recent study There are 25 subj

Data has been analyzed from a recent study. There are 25 subjects in the sample. The mean is 75, standard deviation is 4.7. Answer the following....

a- What is the standard error o the mean for these data?

b- what are the 95% and 99% confidence intervals?

c- What is the probability of obtaining by chance the following: a mean less than 72? a mean less than 74? a mean greater than 76? and a mean greater than 78?

Solution

a)
Mean(x)=75
Standard Error= sd/ Sqrt(n)
Where,
sd = Standard Deviation
n = Sample Size

Standard deviation( sd )=4.7
Sample Size(n)=25
Standard Error = ( 4.7/ Sqrt ( 25) )
= 0.94
b)
AT 0.05
Confidence Interval
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
Standard deviation( sd )=4.7
Sample Size(n)=25
Confidence Interval = [ 75 ± t a/2 ( 4.7/ Sqrt ( 25) ) ]
= [ 75 - 2.0639 * (0.94) , 75 + 2.0639 * (0.94) ]
= [ 73.06,76.94 ]

AT 0.01
Confidence Interval = [ 75 ± t a/2 ( 4.7/ Sqrt ( 25) ) ]
= [ 75 - 2.7969 * (0.94) , 75 + 2.7969 * (0.94) ]
= [ 72.37,77.63 ]

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