Question

Does drying barley seeds in a kiln increase the yield of barley? A famous

experiment by William S. Gosset (who discovered the t distributions) investigated this

question. Eleven pairs of adjacent plots were marked out in a large field. For each pair,

regular barley seeds were planted in one plot and kiln-dried seeds were planted in the

other. A coin flip was used to determine which plot in each pair got the regular barley seed

and which got the kiln-dried seed. The following table displays the data on barley yield

(pound per acre) for each plot.

Do these data provide convincing evidence at the α=0.05 level

that drying barley seeds in a kiln increases the yield of barley, on average?

Short answer

The actual mean difference (regular–kiln dried) in yield between regular barley seeds and kiln-dried seeds is less than 0.

Step-by-step solution

given information

sample size = 10.

significance level = 0.05

we have to find that drying barley seeds in a kiln increases the yield of barley, on average

Hypotheses

The actual mean difference in yield between regular barley seeds and kiln-dried seeds is 0.

The actual mean difference in yield between regular barley seeds and kiln-dried seeds is less than 0.

samples are taken as random

Normal: n = 50 > 30.

The number of employees in this company is > 10 (50) = 500.

Calculations

Perform a t-test

df = 50 – 1 = 49 P-value = 0.01856

p (0.019 0.05), so we reject h0.