8.5-1. A certain size of bag is designed to hold 25 pounds of potatoes. A farmer...
8.5-1. A certain size of bag is designed to hold 25 pounds of potatoes. A farmer fills such bags in the field. Assume that the weight X of potatoes in a bag is N(μ, 9). We shall test the null hypothesis H0: μ = 25 against the alternative hypothesis H1: μ < 25. Let X1, X2, X3, X4 be a random sample of size 4 from this distribution, and let the critical region C for this test be defined by x ≤ 22.5, where x is the observed value of X. (a) What is the power function K(μ) of this test? In particular, what is the significance level α = K(25) for your test? (b) If the random sample of four bags of potatoes yielded the values x1 = 21.24, x2 = 24.81, x3 = 23.62, and x4 = 26.82, would your test lead you to accept or reject H0? (c) What is the p-value associated with x in part (b)?
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8.5-1. A certain size of bag is designed to hold 25 pounds of
potatoes. A farmer...
5. A certain size bag is designed to hold 25 pounds of potatoes. A farmer fills...
5. A certain size bag is designed to hold 25 pounds of potatoes. A farmer fills such bags in the field. Assume that the weight Y of potatoes in a bag follows N(u,9). We would like to test Ho 25 vs. H <25. Let Yi, Y2, Y, Y, be a random sample of size 4 from this distribution, and let the rejection region for this test is Y 22.5 (a) What is the significance level of this test? (b) What...
If a null hypothesis is rejected at a significance level of 1%, then we should say...
If a null hypothesis is rejected at a significance level of 1%,
then we should say that it was rejected at 1%. Reporting that the
null was also rejected at the 5% level of significance is
unnecessary and unwise.
True
False
The p-value equals alpha, the level of significance of the
hypothesis test.
True
False
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING
INFORMATION:
Let X1, X2,
X3, and X4 be a random
sample of observations from a population with...
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution...
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution with mean ?. Consider the test Ho : ?-2.6 vs. H 1 : ? < 2.6. a)Find the best rejection region with the significance level a closest to 0.10 b) Find the power of the test from part (a) at ?= 2.0 and at ?=1.4. c) Suppose x1-1, x2-2, x3 -0, x4-1, x5-2. Find the p-value of the test.
Let X 1, X 2, X 3, X 4 be a random sample of size n=4...
Let X 1, X 2, X 3, X 4 be a random sample of size n=4 from a Poisson distribution with mean . We wish to test Ho: I = 3 vs. H1: \<3. a) Find the best rejection region with the significance level a closest to 0.05. Hint 1: Since H1: X< 3, Reject Ho if X 1+X 2 +X 3 +X 4<= 0 Hint 2: X 1+X 2 +X 3 + X 4 ~ Poisson (4) Hint 3:...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...
Use SPSS for this exam, be sure to include all the following information to get full credits: (1) null and alternative hypotheses (15%) (2) nameofthe test(15%, explain why you chose it) (3) th...
Use SPSS for this exam, be sure to include all the following information to get full credits: (1) null and alternative hypotheses (15%) (2) nameofthe test(15%, explain why you chose it) (3) thetest statistic and its degree offreedom or ANOVAtable(if applicable) (30%! (4) p-value (15%), and (5) scientific conclusion (25%, using 0.05 significance). 1. Ostriches live in hot environments, and they are normally exposed to the sun for long periods Mammals in similar environments have special mechanisms for reducing the...
5. A certain size bag is designed to hold 25 pounds of potatoes. A farmer fills such bags in the field. Assume that the weight Y of potatoes in a bag follows N(u,9). We would like to test Ho 25 vs. H <25. Let Yi, Y2, Y, Y, be a random sample of size 4 from this distribution, and let the rejection region for this test is Y 22.5 (a) What is the significance level of this test? (b) What...
If a null hypothesis is rejected at a significance level of 1%,
then we should say that it was rejected at 1%. Reporting that the
null was also rejected at the 5% level of significance is
unnecessary and unwise.
True
False
The p-value equals alpha, the level of significance of the
hypothesis test.
True
False
THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING
INFORMATION:
Let X1, X2,
X3, and X4 be a random
sample of observations from a population with...
2.Let Xj,X,, Xj, X4, Xj be a random sample of size n-5 from a Poisson distribution with mean ?. Consider the test Ho : ?-2.6 vs. H 1 : ? < 2.6. a)Find the best rejection region with the significance level a closest to 0.10 b) Find the power of the test from part (a) at ?= 2.0 and at ?=1.4. c) Suppose x1-1, x2-2, x3 -0, x4-1, x5-2. Find the p-value of the test.
Let X 1, X 2, X 3, X 4 be a random sample of size n=4 from a Poisson distribution with mean . We wish to test Ho: I = 3 vs. H1: \<3. a) Find the best rejection region with the significance level a closest to 0.05. Hint 1: Since H1: X< 3, Reject Ho if X 1+X 2 +X 3 +X 4<= 0 Hint 2: X 1+X 2 +X 3 + X 4 ~ Poisson (4) Hint 3:...
Problem 2. Consider the following joint probabilities for the two variables X and Y. 1 2 3 .14 .25 .01 2 33 .10 .07 3 .03 .05 .02 Find the marginal probability distribution of Y and graph it. Show your calculations. b. Find the conditional probability distribution of Y (given that X = 2) and graph it. Show your calculations. c. Do your results in (a) and (b) satisfy the probability distribution requirements? Explain clearly. d. Find the correlation coefficient...
Use SPSS for this exam, be sure to include all the following information to get full credits: (1) null and alternative hypotheses (15%) (2) nameofthe test(15%, explain why you chose it) (3) thetest statistic and its degree offreedom or ANOVAtable(if applicable) (30%! (4) p-value (15%), and (5) scientific conclusion (25%, using 0.05 significance). 1. Ostriches live in hot environments, and they are normally exposed to the sun for long periods Mammals in similar environments have special mechanisms for reducing the...
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