SOLUTION: Suppose that you wish to obtain a 95% conÖdence interval for a population mean. The population is normally distributed, the sample size is 20, and the population standard deviation
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Question 1127402: Suppose that you wish to obtain a 95% conÖdence interval for a population mean. The population is normally distributed, the sample size is 20, and the population standard deviation is unknown. The correct procedure to use is the t-interval procedure.
(a) If you mistakenly use the z-interval procedure, will the resulting conÖdence interval be too wide or too narrow? Why?
(b) Will the true conÖdence level associated with this interval be greater than or less than 95%? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! The t-value for a given df is always larger than the z value. Since the confidence interval is proportional to the z/t-value, it will be smaller than it should be if the smaller z-value is used.
The true confidence interval associated with the interval will be less than 95%. Because it is narrower than it should be, there is more likelihood the true value of the parameter will lie outside the CI.
