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Please provide the following information for Problems 11-22. part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii)Check Requirements What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(iii)Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv)Based on your answers in parts (i)—(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
(v)Interpret your conclusion in the context of the application.
Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount, and therefore produce a slightly more “conservative” answer. Answers may vary due to rounding.
Agriculture: Bell Peppers The pathogen Phytophthora capsici causes bell peppers to wilt and die. Because bell peppers are an important commercial crop, this organism has undergone a great deal of agricultural research. It is thought that too much water aids the spread of the pathogen. Two fields are under study. The first step in the research project is to compare the
Field A samples,
| 10.2 | 10.7 | 15.5 | 10.4 | 9.9 | 10.0 | 16.6 |
| 15.1 | 15.2 | 13.8 | 14.1 | 11.4 | 11.5 | 11.0 |
Field B samples,
| 8.1 | 8.5 | 8.4 | 7.3 | 8.0 | 7.1 | 13.9 | 12.2 |
| 13.4 | 11.3 | 12.6 | 12.6 | 12.7 | 12.4 | 11.3 | 12.5 |
Use a calculator with mean and standard deviation keys to verify that
(a) Assuming the distribution of soil water content in each field is mound-shaped and symmetrical, use a 5% level of significance to test the claim that field A has, on average, a higher soil water content than field B.
(b) Find a 90% confidence interval for
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Chapter 10 Solutions
Understanding Basic Statistics
- 8- 6. Show that, for any random variable, X, and a > 0, 8 心 P(xarrow_forward15. This problem extends Problem 20.6. Let X, Y be random variables with finite mean. Show that 00 (P(X ≤ x ≤ Y) - P(X ≤ x ≤ X))dx = E Y — E X.arrow_forward(b) Define a simple random variable. Provide an example.arrow_forward17. (a) Define the distribution of a random variable X. (b) Define the distribution function of a random variable X. (c) State the properties of a distribution function. (d) Explain the difference between the distribution and the distribution function of X.arrow_forward16. (a) Show that IA(w) is a random variable if and only if A E Farrow_forward15. Let 2 {1, 2,..., 6} and Fo({1, 2, 3, 4), (3, 4, 5, 6}). (a) Is the function X (w) = 21(3, 4) (w)+711.2,5,6) (w) a random variable? Explain. (b) Provide a function from 2 to R that is not a random variable with respect to (N, F). (c) Write the distribution of X. (d) Write and plot the distribution function of X.arrow_forward20. Define the o-field R2. Explain its relation to the o-field R.arrow_forward7. Show that An → A as n→∞ I{An} - → I{A} as n→ ∞.arrow_forward7. (a) Show that if A,, is an increasing sequence of measurable sets with limit A = Un An, then P(A) is an increasing sequence converging to P(A). (b) Repeat the same for a decreasing sequence. (c) Show that the following inequalities hold: P (lim inf An) lim inf P(A) ≤ lim sup P(A) ≤ P(lim sup A). (d) Using the above inequalities, show that if A, A, then P(A) + P(A).arrow_forward19. (a) Define the joint distribution and joint distribution function of a bivariate ran- dom variable. (b) Define its marginal distributions and marginal distribution functions. (c) Explain how to compute the marginal distribution functions from the joint distribution function.arrow_forward18. Define a bivariate random variable. Provide an example.arrow_forward6. (a) Let (, F, P) be a probability space. Explain when a subset of ?? is measurable and why. (b) Define a probability measure. (c) Using the probability axioms, show that if AC B, then P(A) < P(B). (d) Show that P(AUB) + P(A) + P(B) in general. Write down and prove the formula for the probability of the union of two sets.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
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