SOLUTION: Suppose that you wish to obtain a 95% confidence interval for a population mean. The population is normally distributed, the sample size is 20, and the population standard deviatio

Algebra.Com
Question 1108899: Suppose that you wish to obtain a 95% confidence 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 confidence interval be too wide or too narrow? Why?
(b)Will the true confidence level associated with this interval be greater than or less than 95%?

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
sample size is 20.

z-score for 95% confidence interval would be plus or minus 1.959963986.

t-score for 95% confidence interval would be plus or minus 2.093024022, using 19 degrees of freedom (sample size of 20 - 1 = 19 degrees of freedom).

if you mis-understood the z-score to be the t-score, the resulting confidence interval would be too narrow.

if the z-score was interpreted as the t-score, then a t-score of plus or minus 1.959963986 with 19 degrees of freedom would generate a confidence level of .9351665248 = 93.5%.

that would be less than the desired 95%.




RELATED QUESTIONS

Suppose that you wish to obtain a 95% conÖdence interval for a population mean. The... (answered by Boreal)
Given a normally distributed population, find a 95% confidence interval for the... (answered by Fombitz)
We use the t distribution to construct a confidence interval for the population mean when (answered by Theo)
In a random sample of 26 computers, the mean repair cost was $130 with a sample standard... (answered by stanbon)
if x bar equals 75, S equals 24, and n equals 36, and assuming that the population is... (answered by Fombitz)
In a random sample of 29 ​people, the mean commute time to work was 34.2 minutes... (answered by Boreal)
In a random sample of 25 people, the mean commute time to work was 33.8 minutes and the... (answered by jim_thompson5910)
5.7 Suppose that the population standard deviation (sigma) for a normally distributed... (answered by stanbon,ewatrrr)
Construct a 95% confidence interval for the population mean μ (answered by ikleyn)