1 pt A random sample of 12 size AA batteries for toys yield

(1 pt) A random sample of 12 size AA batteries for toys yield a mean of 3.07 hours with standard deviation, 0.75 hours.

(a) Find the critical value, t*, for a 99% CI. t* =

(b) Find the margin of error for a 99% CI =

Solution

a)

As

df = n - 1 = 11

alpha/2 = (1 - confidence level)/2 =    0.005          
Thus, by table/technology,

t(alpha/2) = critical t for the confidence interval =    3.105806516   [ANSWER]

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b)      

Note that              

Margin of Error E = t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
t(alpha/2) = critical t for the confidence interval =    3.105806516          
s = sample standard deviation =    0.75          
n = sample size =    12          
df = n - 1 =    11          

Thus,              

Margin of Error E =    0.672426835   [ANSWER]