Degrees of Freedom of a Known Test 2 points possible graded) Let us consider a statistical...
a) true b) false 42. For a chi-square distributed random variable with 10 degrees of freedom and a level of sigpificanoe computed value of the test statistics is 16.857. This will lead us to reject the null hypothesis. a) true b) false 43. A chi-square goodness-of-fit test is always conducted as: a. a lower-tail test b. an upper-tail test d. either a lower tail or upper tail test e. a two-tail test 44. A left-tailed area in the chi-square distribution...
5. Using the Kolmogorov-Smirnov two-sample test, show that the t statistic with large degrees of freedom can be approximated by the standard normal distribution. How large should the degrees of freedom be? Hint: Do simulations on a large sample.
Let T have a (Student's) t distribution with 10 degrees of freedom. If P(T < k) = 0.95, what is the value of k? Let mu be the unknown mean of a Normal distribution. I take 20 observations randomly from this distribution, and want to test H0: mu = 15 vs H1: mu is not equal to 15 at the 5% level of significance. If I observe a p-value of 0.11, what decision can I make? Write mu for the...
As on the previous page, let Xi,...,Xn be i.i.d. with pdf where >0 2 points possible (graded, results hidden) Assume we do not actually get to observe X, . . . , Xn. to estimate based on this new data. Instead let Yİ , . . . , Y, be our observations where Yi-l (X·S 0.5) . our goals What distribution does Yi follow? First, choose the type of the distribution: Bernoulli Poisson Norma Exponential Second, enter the parameter of...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d./. that is smaller. In some situations, this choice of d.l. may increase the P-value by a small amount and therefore produce a slightly more conservative answer Is fishing better from a boat or from the shore? Pyramid Lake is located on the Palute Indian Reservation in Nevada, Presidents, movie stars, and people...
2. Let Xi, , Х, be a random sample gamma(a, β). In parts (a-(d) assume a is known. 30 points a. Consider testing H. : β--βο. Derive Wald statistic for testing H, using the MLE of B both in the numerator and denominator of the statistic. b. Derive a test statistic for testing H, using the asymptotic distribution of the MLE of β. What is the relation between the two statistics in parts (a) and (b)? c. Derive the Score...
Below is the output from an ANOVA test Note that the degrees of
freedom between groups is 2,
The degrees of freedom within is given to be 39, the F statistic
is given to be 3.33. and the p-value of
0.0461. (a) How many groups are there in this test? (b) What was
the sample size? (c) What is the conclusion of the test at the 5%
significance level?
An independent random sample is selected from an approxi- mately
normal...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom dl. not in the Student's t table, use the dosest d.. that is smaller, In some situations, this choice of d.l. may increase the P-value by a small amount and therefore produce a slightly more "conservative answer. Is fishing better from a boat or from the shore? Pyramid Lake is located on the Palute Indian Reservation in Nevada. Presidents, movie stars, and people...
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smalier. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are...
As on the previous page, let X1,... ,Xn be iid with pdf where θ > 0. (to) 2 Possible points (qualifiable, hidden results) Assume we do not actually get to observe Xı , . . . , X. . Instead let Yı , . . . , Y, be our observations where Yi = 1 (Xi 0.5) . Our goal is to estimate 0 based on this new data. What distribution does Y follow? First, choose the type of distribution:...