In: Statistics and Probability
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean is found to be 108, and the sample standard deviation is found to be 10. Construct the 96% confidence interval if the sample size is 25.
a. Construct the 96% confidence interval if the sample size is 10.
b. How does decreasing the sample size affect the margin of error?
c.Could you have computed the confidence intervals in a. and b.
d. if the population was not normal? Explain your answer.
(a)
(b)
(c)
Margin of error increases when sample size decreases.
(d)
No, we cannot compute the confidence intervals from part (a)- (b) if it is not stated that the population is not been normally distributed.
Whenever we have the information regarding the population standard deviation \left( \sigma \right)(σ) then we use the normal distribution.