Let α1 = 1 - 0.90 = 0.1. α2 = 1-0.95=0.05, α3 = 1 - 0.99=0.01 are significance levels, degree of freedom
d = 25 - 1 = 24.
For α1 = 0.1 and d = 24 critical t-value t1 = 1.711.
For α2 = 0.05 and d = 24 critical t-value t2 = 2.064,
For α3 = 0.1 and d = 24 critical t-value t3 = 2.797.
We will find corresponding confidence intervals, using expression
"where\\ \\mu\\ is \\ sample\\ mean ,\\ t\\ is\\ a\\ critical\\ value,"
"n\\ is\\ the\\ size\\ and\\ s\\ is\\ standard\\ deviation\\ of\\ the\\ sample."
a) Confidence interval is
"(80-10.266,\\ 80+10.266)="
"(69.734,\\ 90.266)"
b) Confidence interval is
"(80-12.384,\\ 80+12.384)="
"(67.616,\\ 92.384)"
c) Confidence interval is
"(80-16.782,\\ 80+16.782)="
"(63.218,\\ 96.782)"
Answer: a) (69.734, 90.266), b) (67.616, 92.384), c) (63.218, 96.782)
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