1 Suppose that you are planning a greenhouse experiment on t

1. Suppose that you are planning a greenhouse experiment on the growth of pepper plants to determine if a specially treated soil promotes growth. You will grow n individual plotted seedlings in specially treated soil and after 21 days you will measure the length of each plant, and then conduct a t-test with alpha = .01. Data from a pilot study in standard soil gave y-bar =12.5 cm and s = 0.7 cm. It is important for you to detect if the effect of the specially treated soil is to increase the stem length by 1.0 cm, so you would like to have .95 power to detect such an increase.

USE T-test table to find sample size

Solution

Given that y bar = 12.5 and s = 0.7 cm.

The stem length should be increased by 1 cm.

Confidence level = 99%

As degree of freedom is given as n-1 we cannot precisely determine the sample size as per t test.

Let us assume n is sufficiently large so that this distribution becomes almost normal

Margin of error = 0.05 = 2.58sigma /rtn = 2.58(0.7)/rtn

Hence rt n = 36.12

n = 1304.6

Hence sample size should be atleast 1305.