GATE 2024 ES – Question 36
Ten observations are drawn from a normal population with mean µ. Their mean is x and standard deviation S. The supplied Student-t table lists rows D=9,10,11 and columns cumulative probability .90,.95,.975,with values(1.38,1.83,2.26),(1.37,1.81,2.23),(1.36,1.80,2.20). Which interval is used for a two-sided10% test of $H_0:\mu=0$?
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Correct answer: (B) $-1.83<x/(S/\sqrt{N-1})<1.83$
Explanation
Estimate one population mean from N=10 observations, so degrees of freedom are9. A two-sided10% test leaves5% in each tail and uses the.95 quantile,1.83 in row9. Thus the intended nonrejection interval is **B**. The printed statistic uses $S/\sqrt{N-1}$,consistent if S is computed with divisor N. If S means the usual unbiased sample standard deviation, the conventional denominator is $S/\sqrt N$ instead. That normalization ambiguity is retained rather than silently changing every option.