Question

You may need to use the appropriate appendix table or technology to answer this question. A sample of 121 checked bags at an airport had an average weight of 41 pounds with a standard deviation of 5 pounds.

(a) At 95% confidence, compute the margin of error (in pounds). (Round your answer to four decimal places.) ▭ lbs
Explain what it shows.
We can say with 0.95 probability that the distance between the sample mean of 41 pounds and the population mean is at least the margin of calculi
We can say with 0.95 probability that the distance between the sample mean of 41 pounds and the population mean is at most the margin of error calcul
(b) Determine a 95% confidence interval for the population mean weight of checked bags at the airport (in pounds). (Round your answers to two decimal places.) lbs▭ to ▭ lbs

Answer 1

To compute the margin of error at a 95% confidence level, we use the formula Margin of Error = Z * (Standard Deviation / √(n)), where Z is the z-value for the desired confidence level. The margin of error represents the maximum amount by which the sample mean can differ from the population mean while still being within the desired confidence level. The 95% confidence interval for the population mean weight of checked bags at the airport is approximately 40.1552 to 41.8448 pounds.

Step-by-step explanation:

To compute the margin of error, we can use the formula:

Margin of Error = Z * (Standard Deviation / √(n))

where Z is the z-value corresponding to the desired confidence level, Standard Deviation is the standard deviation of the sample, and n is the sample size.

For a 95% confidence level, the z-value is approximately 1.96. Plugging in the values, we get:

Margin of Error = 1.96 * (5 / √(121))

Calculating this, we find that the margin of error is approximately 0.8448 pounds.

The margin of error represents the maximum amount by which the sample mean can differ from the population mean while still being within the desired confidence level.

To determine the confidence interval for the population mean weight of checked bags at the airport, we can use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Plugging in the values, we get:

Confidence Interval = 41 ± 0.8448

Calculating this, we find that the 95% confidence interval for the population mean weight of checked bags at the airport is approximately 40.1552 to 41.8448 pounds.