Consider 25 ± 1 (n=5) and 26 ± 1 (n=6); The uncertainty listed is the standard...

Consider 25 ± 1 (n=5) and 26 ± 1 (n=6); The uncertainty listed is the standard deviation. Are these two measurements significantly different at the 95% confidence limit ?

Expert Solution

25 ± 1 (n=5)

mean = x = 25

standard deviation = 1

n = 5

confidence interval = x + t.S/ sqrt(n)

= 25 + 2.776 x 1 / sqrt(5)

= 25 + 1.24

26 ± 1 (n=6)

n = 6

if n = 6 degrees of freedom = n-1 = 5 at 95% the t- value = 2.571

confidence interval = x + t.S/ sqrt(n)

= 26 + 2.571 x 1 / sqrt(6)

= 26 + 1.049

yes , these two measurements significantly different at the 95% confidence limit

queen_honey_blossom answered 5 months ago

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