Final answer:
To find the margin of error and 95% confidence interval for the percentage of bean plants that show increased growth after applying the fertilizer, calculate the standard error, multiply it by the critical value, and add/subtract the result from the sample percentage. In this case, the margin of error is 6.6403 and the confidence interval is 9.3597% to 22.6403%.
Step-by-step explanation:
To find the margin of error and 95% confidence interval for the percentage of all bean plants that show increased growth after applying the fertilizer, you will need to use the formula for confidence intervals:
Confidence Interval = Sample Percentage ± Margin of Error
To calculate the margin of error, you will need to multiply the standard error and the critical value.
The standard error is the square root of (Sample Percentage * (100 - Sample Percentage) / Sample Size).
The critical value can be found using a Z-table or a calculator. For a 95% confidence level, the critical value is approximately 1.96.
Let's calculate:
Sample Percentage = 16
Sample Size = 142
Standard Error = sqrt((16 * (100 - 16)) / 142) = 3.3877
Critical Value = 1.96
Margin of Error = Standard Error * Critical Value = 3.3877 * 1.96 = 6.6403
Confidence Interval = 16 ± 6.6403 = 9.3597 to 22.6403