Suppose you take a random samp
Suppose you take a random sample of 30 individuals from a largepopulation. For this sample, the sample mean is 4.2 and samplevariance is 49. You wish to estimate the unknown population meanµ.
(a) Calculate a 90% confidence interval for µ.
(b) Calculate a 95% confidence interval for µ.
(c) Based on (a) and (b), comment on what happens to the widthof a confidence interval (increase/decrease) when you increase yourconfidence level.
(d) Suppose your sample size is 100 instead of 30. The samplemean and variance are still 4.2 and 49 respectively. Calculate anew 90% confidence interval for µ.
(e) Based on (a) and (d), comment on what happens to the widthof a confidence interval (increase/decrease) when you increase yoursample size.
Answer:
Given that
sample n =30
sample mean μ,=4.2
sample variance σ^2= 49
standard deviation σ = 7
a)
b)
c) The width increases as the confidence levelincrease
d)
e)
Increasing the sample size decreases the width of confidenceintervals
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