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Confidence Interval for the Mean of Nervousness

You have been research for your statistics class on how nervous the American adults are in general, you have decided to use HINTS 2007 data set that has a scale (going from 0 to 24)measuring the psychological distress of the respondents.
a. According to HINTS 2007 data, the average psychological distress score, for this sample size of 1,390, is 4.75, with a standard deviation of 4.5. Construct the 95 % confidence interval for the true psychological distress of the respondents.
b. One of your classmates, who claims to be good at statistics, complaint about your confidence interval calculation. She asserts that the psychological distress scores are normally distributed, which in turns makes the confidence interval calculation meaningless. Assume that she is correct about her distribution of psychological distress scores. Does that imply that the calculation of a confidence interval is not appropriate? why?or why not?

Solution Summary

The solution contains step-by-step calculation of confidence interval for the mean and detailed discussion about confidence intervals and normal distribution.