Question

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment. An experiment is conducted to compare peach-tree seedling growth when the soil and weeds are treated with one of two herbicides. In a field containing 20 seedlings, 10 are randomly selected throughout the field and assigned to receive herbicide A. The remainder of the seedlings is assigned to receive herbicide B. Soil and weeds for each seedling are treated with the appropriate herbicide, and at the end of the study period, the height in centimeters is recorded for each seedling. The following results are obtained: Herbicide A = 94.5 cm s1 = 10 cm Herbicide B = 109.1 cm s2 = 9 cmWhat is a 90% confidence interval (use the conservative value for the degrees of freedom) for μ2 – μ1?

a. 14.6 ± 7.00
b. 14.6 ± 7.38
c. 14.6 ± 7.80
d. 14.6 ± 9.62

Answer 1

A. 14.6 ± 7.00

Explanation:

Formula for the confidence interval between the two mean is;

CI = (μ2 - μ1) ± z√[((s1)²/n1) + ((s2)²/n2)]

We are given;

μ1 = 94.5

μ2 = 109.1

s1 = 10

s2 = 9

n1 = 10

n2 = 10

The z-value at confidence interval of 90% is 1.645

Thus;

CI = (109.1 - 94.5) ± 1.645√[(10²/10) + (9²/10)]

CI = 14.6 ± 7.00