Calculate the confidence interval for a sample mean.

Published on February 11, 2025

Statistics

The 95% confidence interval for the population mean is approximately [13.984, 14.416]

Question

not correct 13.984 ; 14.416 kannst du damit was anfangen?

Here’s how to calculate the confidence interval for the population mean

1. Identify the given information:

From the problem description and tables, we have:

2. Determine the appropriate distribution:

Since the population standard deviation

is known and the population is normally distributed, we use the standard normal distribution (z-distribution) to calculate the confidence interval.

3. Find the critical value :

For a 95% confidence interval,

, so

, and

.
We need to find the z-value

from the given table or a standard normal distribution table.
From the provided table, we find

4. Calculate the margin of error (E):

The margin of error for the confidence interval is given by:

Plugging in the values:

5. Calculate the confidence interval:

The confidence interval is given by:

Plugging in the values:

6. Round to three decimal places:

Rounding to three decimal places, we get the confidence interval:

Therefore, the 95% confidence interval for the population mean

is approximately [13.984, 14.416].

Konfidenzintervall: [

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