Question

The company alters their toy-building machines and wants to run another sample. This time, they would like the margin of error to be less than 0.6 inches for a 95

Answer 1

To achieve a margin of error less than 0.6 inches with a 95% confidence level, the company should run a sample size of at least 61 toys.

Step-by-step explanation:

To find the required sample size, we need to use the formula:

n = (Z * σ / E)²

Where:

• n is the required sample size
• Z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence level is 1.96)
• σ is the standard deviation of the population (unknown here)
• E is the desired margin of error (0.6 inches)

Since the standard deviation is unknown, we can estimate it using the margin of error.

σ ≈ E / Z = 0.6 / 1.96 ≈ 0.3061 inches

Now we can substitute the values into the formula:

n = (1.96 * 0.3061 / 0.6)² ≈ 60.114

Therefore, the company should run a sample size of at least 61 toys to achieve a margin of error less than 0.6 inches with a 95% confidence level.