Question

SeedLanc is a seed company leader in maize seeds. The current line of maize seeds (traditional) yields 150 kilogrammes per hectare. The company believe they have produced an improved line of maize seeds (called ‘gold line’) and would like to test the yield per hectare under standard farming conditions on farms selected at random in Lancashire.

a. What should be the (smallest) sample size to have an accurate estimate for the gold line yield? Specifically, the company would like to have a margin of error for the 95% confidence interval of at most 12.5 kilograms per hectare, assuming that the standard deviation for maize yields is known to be 25.51. Justify your answer. What assumptions do you need to make for your answers to be accurate? [25 Marks]

b. SeedLanc decided to test the gold line in 30 farms. The yields had a sample mean of 186 kilogrammes per hectare and a sample standard deviation of 20.1. If the company considers a line to be an improvement over another only for productivity gains above 20%, propose and carry out a test to investigate whether the gold line is in fact an improvement over the traditional one. Use a 5% significance level. State your conclusion clearly in layman’s (i.e. non-statistical) terms. What assumptions have been necessary to be accurate? [30 Marks]

c. Obtain the power of the statistical test used in part (b) if the true mean for gold line is 190 kilogrammes per hectare. [30 Marks]

Answer 1

A) Required Sample size(n) = ((1.96* s)^2)/L^2

where

L is the allowable error in the variable being measured,

s is the standard deviation of the observations,

n is the required sample size (number of observations).

Here L = 12.5 kilograms per hectare,

s= 25.51

So, n = 2499.96000016 / 156.25    = 15.999744001 ~ 16

So, sample size is 16.

B)