Question
In: Statistics and Probability
1. A stress level study based on a random sample of 49 undergraduates at your university...
1. A stress level study based on a random sample of 49 undergraduates at your university reported a mean of 73 (on a 0-100 scale). Assume the population standard deviation is 28.
(a) Find the margin of error for an 80%, 90%, 95%, and 99% confidence interval. Draw a diagram with the confidence intervals, and summarize the effect of the confidence level on the margin of error.
(b) Now consider changing the sample size, but assume that the sample mean is still 73. Find the margin of error for a 95% confidence interval using the following sample sizes: 10, 20, 40, and 80. Draw a diagram with the confidence intervals, and summarize the effect of the sample size on the margin of error.
Solutions
Expert Solution
As confidence level increases the margin of error increases and hence width of confidence interval increases.
(b)
As sample size increases the margin of error decreases and hence width of confidence interval decreases.
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