Question
In: Statistics and Probability
Using R Studio Use the two iid samples. (You can copy and paste the code into...
Using R Studio
Use the two iid samples. (You can copy and paste the code into R). They both come from the same normal distribution.
X = c(-0.06, 1.930, 0.608 -0.133,0.657, -1.284, 0.166, 0.963, 0.719, -0.896)
Y = c(0.396, 0.687, 0.809, 0.939, -0.381, -0.042, -1.529, -0.543, 0.758, -2.574, -0.160, -0.713, 0.311, -0.515, -2.332, -0.844, -0.942, 0.053, 0.066, 0.942, -0.861, -0.186, -0.947, -0.110, 0.634, 2.357, 0.201, -0.428, -1.661, 0.395)
(a) Report 95% confidence interval for the mean of X. Should we use t-CI or z-CI?
(b) Report 95% confidence interval for the mean of X, if we have already known the population variance is 1. Should we use t-CI or z-CI?
(c) Report 90% confidence interval (t-CI) for the mean of Y .
(d) Report 95% confidence interval (t-interval) for the mean of Y and compare the result with the result in part (c). Describe the relationship between the confidence level and the width of the CI.
(e) Assuming the CIs reported in (a) and (c) are valid, compare the result of (a) and (c) and describe the relationship between the sample size and the width of the CI.
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