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A random sample of 41 observations was selected from a normally distributed population. The sample mean was [tex]\bar{x} = 97.7[/tex], and the sample variance was [tex]s^2 = 35.3[/tex].

Answer :

The standard error of the sample mean is approximately s/√n = √(s²/n) = √(35.3/41) ≈ 0.759.

To calculate the standard error of the sample mean (SEM), we use the formula SEM = s/√n, where s is the sample standard deviation and n is the sample size. Given that the sample variance (s²) is 35.3 and the sample size (n) is 41, we can plug these values into the formula to find the SEM. Substituting the values, we get SEM ≈ √(35.3/41) ≈ √(0.861) ≈ 0.759.

The standard error of the sample mean measures the precision with which the sample mean estimates the population mean. A smaller standard error indicates that the sample mean is a more reliable estimate of the population mean. In this case, with a standard error of approximately 0.759, we can expect the sample mean of 97.7 to be within 0.759 units of the population mean on average.

Therefore, the standard error of the sample mean for the given sample is approximately 0.759.

Correct option: √(35.3/41) ≈ 0.759

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