Question

Scientists conducted a research and found that conducted that parsley plants takes nutrients from the soil. In 2015, 19.7 percent of 61 randomly selected parsley plant. In 2018, 38.5 percent of 52 randomly selected parsley plants were taking nutrient from the soil. (a) Assume that all conditions for inference have been checked and verified.

a. Construct a 95% confidence interval for the difference in the proportions of all parsley plants took nutrient  in 2014 and 2019. Round your final answer to 3 decimal places.

b. ) Does the confidence interval in part (a) provide convincing statistical evidence that there has been an increase in the proportion of all parsely plants that are taking nutrient from the soil? Explain

Answer 1

a) p₂₀₁₄ = 0.197, p₂₀₁₈ = 0.385

Let difference = p₂₀₁₈ - p2014

Pooled proportion () = (0.197*61 + 0.385*52) / (61 + 52) = 0.2835

For 95% confidence, z = 1.96

Hence,

95% confidence interval for difference in proportions will be:

(0.021, 0.355)

b) Since the interval only contains positive values, there is sufficient evidence to conclude that there has been an increase in the proportion of all parsely plants that are taking nutrient from the soil.