Question

An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil. Out of 155 seeds planted in soil containing 3% mushroom compost by weight, 74 germinated. Out of 155 seeds planted in soil containing 5% mushroom compost by weight, 86 germinated. Let p_X represents the population proportion of seeds germinated in soil containing 5% mushroom compost by weight and let p_Y represents the population proportion of seeds germinated in soil containing 3% mushroom compost by weight. Find a 95% confidence interval for the difference p_X − p_Y  between the proportions of seeds that germinate. (Round the final answers to four decimal places.)

Answer 1

Given that,

For sample 1 : n1 = 155, x = 86 and

For sample 2 : n2 = 155, y = 74 and

A 95% confidence level has significance level of 0.05 and critical value is,

The margin of error (E) is,

The 95% confidence interval for the difference px - py is

Therefore, required confidence interval is, (-0.0335, 0.1883).