Question

A researcher is investigating whether a difference exists in the mean weight of green-striped watermelons grown on two different farms: one that uses organic methods and one that uses non-organic methods. The mean and standard deviation of the weights in a random sample of 43 watermelons from the organic farm were 18 pounds and 2 pounds, respectively. The mean and standard deviation of the weights in a random sample of 40 watermelons from the non-organic farm were 20 pounds and 1.7 pounds, respectively.Which of the following represents the standard error of the difference in the mean weights of watermelons from the two farms? a. 2+1.7b. $\sqrt{243+1.740}$c. $\sqrt{243} + \sqrt{1.740}$d. $\sqrt{2243+1.7240}$e. $\sqrt{22+1.7243+40}$

Answer 1

Answer: The correct option is d

Step-by-step explanation:

Standard error measures how far the sample mean is from the population mean.

The formula for determining the standard error of the distribution of difference in means is expressed as

Standard error = √(s1²/n1 + s2²/n2)

where

s1 = sample 1 standard deviation

s2 = sample 2 standard deviation

n1 = number of samples 1

n2 = number of samples 2

From the information given

s1 = 2 pounds

n1 = 43 pounds

s2 = 1.7 pounds

n2 = 40 pounds

Standard error = √(2²/43 + 1.7²/40)