The 95% confidence interval for the population mean ,given that the sample size n = 49 and the population standard deviation = 7,is .

Question

The 95% confidence interval for the population mean  ,given that the sample size n = 49 and the population standard deviation  = 7,is  .

Quizplus · Accepted Answer

The formula for the confidence interval for the population mean when the population standard deviation is known is given by:

CI = x̄ ± Zα/2 * (σ/√n)

where x̄ is the sample mean, Zα/2 is the critical value from the standard normal distribution for the desired confidence level, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we have:

CI = x̄ ± 1.96 * (7/√49)

Simplifying, we get:

CI = x̄ ± 1.96

Since this is a constant value and not a range, it is a valid 95% confidence interval for the population mean. Therefore, the answer is A)True.

The 95% Confidence Interval for the Population Mean ,Given