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Tests and confidence intervals 0/1 point (graded) Let \( \mathcal{I}=(\hat{a}, \hat{b}) \) be a confidence interval at asymptotic level \( 95 \% \) for an exponential distribution with parameter \( \lambda>0 \). Let \( \psi \) be a test based on this confidence interval for the problem: \[ \Theta=\mathbb{R}, \quad \text { and } \begin{array}{cc} H_{0}: & \lambda=1 \\ H_{1}: & \lambda \neq 1 \end{array} \] Check all that apply. The probability that \( \lambda \) is equal to 1 is at most \( 5 \% \) \( \psi \) rejects \( H_{0} \) at asymptotic level \( 5 \% \) \( \psi \) rejects \( H_{0} \) at asymptotic level \( 10 \% \) \( \mathcal{J}=(\hat{a}-1.1, \hat{b}+6) \) is a confidence interval at asymptotic level \( 95 \% \)

          Tests and confidence intervals
0/1 point (graded)
Let \( \mathcal{I}=(\hat{a}, \hat{b}) \) be a confidence interval at asymptotic level \( 95 \% \) for an exponential distribution with parameter \( \lambda>0 \). Let \( \psi \) be a test based on this confidence interval for the problem:
\[
\Theta=\mathbb{R}, \quad \text { and } \begin{array}{cc}
H_{0}: & \lambda=1 \\
H_{1}: & \lambda \neq 1
\end{array}
\]

Check all that apply.
The probability that \( \lambda \) is equal to 1 is at most \( 5 \% \)
\( \psi \) rejects \( H_{0} \) at asymptotic level \( 5 \% \)
\( \psi \) rejects \( H_{0} \) at asymptotic level \( 10 \% \)
\( \mathcal{J}=(\hat{a}-1.1, \hat{b}+6) \) is a confidence interval at asymptotic level \( 95 \% \)

Tests and confidence intervals
0/1 point (graded)
Let ℐ=(â, b̂) be a confidence interval at asymptotic level 95 % for an exponential distribution with parameter λ>0. Let ψ be a test based on this confidence interval for the problem:

Θ=ℝ, and
H0: λ=1

H1: λ≠ 1

Check all that apply.
The probability that λ is equal to 1 is at most 5 %
ψ rejects H0 at asymptotic level 5 %
ψ rejects H0 at asymptotic level 10 %
𝒥=(â-1.1, b̂+6) is a confidence interval at asymptotic level 95 %

Added by Meredith A.

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