Question

Let 𝑥1, 𝑥2, … , 𝑥10 be the observed values of a random sample of size 10 from an 𝑁(𝜃, 𝜎 2 ) distribution, where 𝜃 ∈ ℝ and 𝜎 > 0 are unknown parameters. If
𝑥̅=$\frac{1}{10}$ $∑^{10}_{i=1}x_i=0$ and s=$\sqrt{\frac{1}{9}∑^{10}_{i=1}(x_i-\overline{x})^2=2,}$
then based on the values of 𝑥̅ and 𝑠 and using Student’s 𝑡-distribution with 9 degrees of freedom, 90% confidence interval(s) for 𝜃 is/are

• A. (−0.8746, ∞)
• B. (−0.8746, 0.8746)
• C. −1.1587, 1.1587)
• D. (−∞, 0.8746)

Answer 1

Answer: (A), (C), (D)

(−0.8746, ∞)

Answer 2

The correct options are: A, C and D