a simple random sample is drawn from a normally - distributed population, and when making a statistical…

a simple random sample is drawn from a normally - distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5.9 at a 95% level of confidence. if the mean of the sample is 18.7, what is the 95% confidence interval for the population mean?\n18.7 ± 5.9\n18.7 ± 9.7\n18.7 ± 11.6\n18.7 ± 15.2

a simple random sample is drawn from a normally - distributed population, and when making a statistical inference about the population mean, the margin of error is found to be 5.9 at a 95% level of confidence. if the mean of the sample is 18.7, what is the 95% confidence interval for the population mean?\n18.7 ± 5.9\n18.7 ± 9.7\n18.7 ± 11.6\n18.7 ± 15.2

Answer

Answer:

18.7 ± 5.9

Explanation:

Step1: Recall confidence - interval formula

The formula for a confidence interval for the population mean when the population standard - deviation is unknown (using a t - distribution) or known (using a z - distribution) is $\bar{x}\pm E$, where $\bar{x}$ is the sample mean and $E$ is the margin of error.

Step2: Identify given values

We are given that the sample mean $\bar{x} = 18.7$ and the margin of error $E = 5.9$ at a 95% level of confidence.

Step3: Calculate confidence interval

Substitute the values into the formula: The 95% confidence interval for the population mean is $18.7\pm5.9$.