How to Calculate a 98% Confidence Interval for Estimating the Population Mean

Use the confidence level and sample data to find a confidence interval for estimating the population. Round your answer to the same number of decimal places as the sample mean.A random sample of 130 full grown lobsters have a mean weight of 21 ounces is the standard deviation of 3.0 ounces. Construct a 98% confidence interval for the population mean.

To construct a confidence interval for estimating the population mean, we will use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / square root of the sample size)

First, let’s calculate the critical value

To construct a confidence interval for estimating the population mean, we will use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / square root of the sample size)

First, let’s calculate the critical value. Since we want a 98% confidence interval, the remaining area outside the interval would be (100% – 98%) / 2 = 1%.

Next, we need to find the corresponding z-score for a 1% area in each tail. Using a standard normal distribution table or a calculator, we find that the critical value for a 1% area is approximately 2.33.

Now, we can substitute the given values into the formula:

Confidence interval = 21 ± (2.33 * 3.0 / √130)

Calculating the standard error (standard deviation divided by the square root of the sample size):

Standard error = 3.0 / √130 ≈ 0.262

Substituting the standard error into the confidence interval formula:

Confidence interval = 21 ± (2.33 * 0.262)

Calculating the confidence interval:

Confidence interval = 21 ± 0.610

Rounded to the same number of decimal places as the sample mean (21), the 98% confidence interval for the population mean is approximately (20.390, 21.610).

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