Question

question 15

in a bolt-manufacturing factory, it is estimated that 3% of the bolts being manufactured will be defective, with a 0.4% margin of error.

choose the statement that correctly describes the confidence interval.

• the percentage of defective bolts is 3% or less.
• the percentage of defective bolts is 3% or more.
• the percentage of defective bolts is between 3% and 4%.
• the percentage of defective bolts is between 2.6% and 3.4%.

Explanation:

Identify the point estimate and margin of error

Using the Confidence Interval and Margin of Error knowledge points

$$
LATEXBLOCK0
$$

Calculate the confidence interval bounds

Using the Confidence Interval and Margin of Error knowledge points

$$
LATEXBLOCK1
$$

State the final interval

Using the Confidence Interval knowledge point

$$ \text{Interval} = [2.6\%, 3.4\%] $$

Answer:

• The percentage of defective bolts is 3% or less.
• The percentage of defective bolts is 3% or more.
• The percentage of defective bolts is between 3% and 4%.
• The percentage of defective bolts is between 2.6% and 3.4%. (Correct answer)