When estimating a population mean μ, where the population standard deviation σ is known, we can:
a. choose a larger z value, construct a wider confidence interval, and achieve a lower confidence level
b. choose a smaller z value, construct a narrower confidence interval, and achieve a higher confidence level
c. define the limits of an interval estimate of μ as x ± zα/2σ/√n
d. define the limits of an interval estimate of μ as x ± tα/2·5/n
(c) define the limits of an interval estimate of ƒÊ as x �} zƒ¿/2ƒÐ/�ãn
Because sigma is known
The correct answer is c.
When estimating a population mean μ with a known population standard deviation σ, we use the z-distribution to construct a confidence interval. The formula for the confidence interval is given by x ± zα/2σ/√n, where x is the sample mean, zα/2 is the critical value from the standard normal distribution corresponding to the desired confidence level, σ is the known population standard deviation, and n is the sample size.
Option a is incorrect because choosing a larger z value actually results in a narrower confidence interval and a higher confidence level. Similarly, option b is also incorrect for the same reason.
Option d is also incorrect because it mentions tα/2·5/n, which is not the correct formula for constructing a confidence interval when the population standard deviation is known. The t-distribution is used when the population standard deviation is unknown and is estimated from the sample. In this case, we use the t-distribution and the formula for the confidence interval would be x ± tα/2·s/√n, where s is the sample standard deviation.
So, the correct answer is c.