Out-of-State Tuitions The out-of-state tuitions (OST) (in dollars) for random samples of both public and private...

  

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Out-of-State Tuitions The out-of-state tuitions (OST) (in dollars) for random samples of both public and private four-year colleges in a New England state are listed. Private Public 13,600 13,495 7,050 9,000 16,590 17,300 6,450 9,758 23,400 12,500 7,050 7,871 16,100 a) Assume normality and we know that from housing authority statistics, the standard deviations of OST among all private colleges and among all public colleges are $4100 and $3600 respectively. Test whether mean OST is the same between public and private colleges at a significance level 10%. b) Give a p-value for the above test in a). c) Find the 95% confidence interval for, where is the mean OST among all private colleges, under normality assumptions and we know the housing authority statistics in a). d) Assume normality and we don't know the housing authority statistics, test whether mean OST is the same between public and private colleges at a significance level 10%. e) Give a p-value for the above test in d). f) Find the Find the 95% confidence interval for, where is the mean OST among all private colleges, under normality assumption only. Out-of-State Tuitions The out-of-state tuitions (OST) (in dollars) for random samples of both public and private four-year colleges in a New England state are listed. Private Public 13,600 13,495 7,050 9,000 16,590 17,300 6,450 9,758 23,400 12,500 7,050 7,871 16,100 a) Assume normality and we know that from housing authority statistics, the standard deviations of OST among all private colleges and among all public colleges are $4100 and $3600 respectively. Test whether mean OST is the same between public and private colleges at a significance level 10%. b) Give a p-value for the above test in a). c) Find the 95% confidence interval for, where is the mean OST among all private colleges, under normality assumptions and we know the housing authority statistics in a). d) Assume normality and we don't know the housing authority statistics, test whether mean OST is the same between public and private colleges at a significance level 10%. e) Give a p-value for the above test in d). f) Find the Find the 95% confidence interval for, where is the mean OST among all private colleges, under normality assumption only.