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Inferential Statisticshard
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In a study of protein folding, a scientist uses the Wald test to evaluate the null hypothesis H0:θ=0.5H_0: \theta = 0.5H0​:θ=0.5 against Ha:θ≠0.5H_a: \theta \neq 0.5Ha​:θ=0.5. The researcher calculates the MLE θ^=0.58\hat{\theta} = 0.58θ^=0.58 with a standard error SE=0.04SE = 0.04SE=0.04. If the Wald statistic is W=(θ^−θ0)2SE2W = \frac{(\hat{\theta} - \theta_0)^2}{SE^2}W=SE2(θ^−θ0​)2​, what is the value of WWW and what can be concluded regarding the null hypothesis at α=0.05\alpha = 0.05α=0.05 (critical value 1.962≈3.841.96^2 \approx 3.841.962≈3.84)?