Question

In a paper “The Probable Error of Mean”, William Gosset, compared yields of head corn in pounds per acre for two preparations of seed. (Source: Biometrica, Vol. VI, No.1, 1908). Using seeds that were kiln-dried, Gosset stated that “with 95% confidence, the population mean yield was between 1611.3 and 2071.7 pounds”. He used a sample of 11 yields of head corn per acre. (a) Determine the sample mean ¯x. (b) Determine the 95% margin of error E. (c) Determine the sample standard deviation s.

Answer 1

Solution :

Given that,

Lower confidence interval = 1611.3

Upper confidence interval = 2071.7

(a)

  = (Lower confidence interval + Upper confidence interval ) / 2

= (1611.3 + 2071.7) / 2

= 1841.5

(b)

Margin of error = E = Upper confidence interval -   = 2071.5 - 1841.5 = 230

Margin of error = E = 230

(c)

sample size = n = 11

Degrees of freedom = df = n - 1 = 11 - 1 = 10

t _/2,df = t_0.025, = 2.228

Margin of error = E = t_/2,df * (s /n)

s = E * n / t_/2,df

= 230 * 11 / 2.228

= 342.4

sample standard deviation = 342.4