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Q33Section B (Section B)33 of 60

One-sided and two-sided confidence intervals

Let x1,x2,…,x10x_1, x_2, \dots, x_{10} be the observed values of a random sample of size 1010 from an N(θ,σ2)N(\theta, \sigma^2) distribution, where θ∈R\theta\in\mathbb{R} and σ>0\sigma > 0 are unknown parameters. If xˉ=110∑i=110xi=0\bar{x}=\frac{1}{10}\sum_{i=1}^{10} x_i = 0 and s=19∑i=110(xi−xˉ)2=2s = \sqrt{\frac{1}{9}\sum_{i=1}^{10}(x_i - \bar{x})^2} = 2, then based on the values of xˉ\bar{x} and ss and using Student's tt-distribution with 99 degrees of freedom, 90%90\% confidence interval(s) for θ\theta is/are

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