In a random sample of eight people the mean commute time to work was 35.5 minutes, and the SD was 7.2, find the t distribution to find the mean margin or error, given 95% confidence intervals for the population mean.
Solution :
Given that,
s =7.2
n =8 Degrees of freedom = df = n - 1 =8 - 1 = 7
a ) At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/
2= 0.05 / 2 = 0.025
t
/2,df = t0.025,7 = 2.365 ( using student t
table)
Margin of error = E = t/2,df
* (s /
n)
= 2.365 * (7.2 /
8)
E= 6.0203
Margin of error = E =6.0203
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