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- Let X1, . . . , Xn ∼ iid Unif(θ1, θ2), where both θ1 and θ2 are unknown. Find the MOM estimator and compare them to the MLE.The critical value for t for n = 10 for a one tail test at α = 5% LOS isAfter testing 40 participants, a significant x2obt of 13.31 was obtained. With a .05 and df 2, how would this result be reported in a publication In your own words please not copied from the internet
- If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.If X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y = X1 + X2 +···+ Xn is a sufficient estimator of the parameter θ.The test statistic of z=2.53 is obtained when testing the claim that pnot ≠0.469. a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the P-value. c. Using a significance level of α=0.10, should we reject Upper H (sub)0or should we fail to reject Upper H (sub)0?
- A researcher is using a two-tailed hypothesis test with α = 0.01 to evaluate the effect of a treatment. If theboundaries for the critical region are t = ± 2.845, then how many individuals are in the sample?A. n = 23B. n = 22C. n = 21D. n = 20E. cannot be determined from the information givenLet X1, . . . , Xn, . . . ∼ iid Bern(θ). Consider the Bayes estimator under squared error loss with the Unif(0,1) prior. Show that this estimator is consistent.A researcher is using a two-tailed hypothesis test with α = .05 to evaluate the effect of a treatment. If the boundaries for the critical region are t = ± 2.080, then how many individuals are in the sample?
- Imagine that you conducted a single-sample t test with 8 participants. For a two-tailed test, the tcv at a = 0.05 would beIf X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y =X1 + 2X2 + X3 is not a sufficient estimator of θ. (Hint:Consider special values of X1, X2, and X3.)Suppose we want to compare the length of hospital stay for patients with the same diagnosis at two different hospitals. The results are shown in Table 9.10. 9.7 Why might a t test not be very useful in this case? 9.8 Carry out a nonparametric procedure for testing the hypothesis that lengths of stay are comparable in the two hospitals.