Chapter 8, Problem 8.12LB

7.  Find the critical value of χ2 based on the given information. H1: σ < 0.629, n=19, and α = .025.

. Let B(t) be standard Brownian motion and let Y(t) be the price of a stock at time t given by the formula: Y(t) = Y(0)exp(.055t +.07B(t)). Show all steps in finding the expression for the probability that Y(5) is greater than 150 given that Y(1) = 100. Assume Y(0) is a given positive constant. (You don’t have to give a final number, just an expression that can be used to find the probability.)

Determine the​ upper-tail critical value tα/2 in each of the following circumstances.

An experiment is conducted to determine the relationship between the amount of a certain drug in the bloodstream and the length of time it takes to react to a stimulus. A random sample of 5 persons who took this drug is selected. The amount of drug in the bloodstream x and the reaction time y in selected persons showed thatAmount of drugs x: 2 1 4 3 5Reaction time y: 1 1 2 2 4Σx=15 , Σx² = 55,  Σy=10,  Σy² = 26,  Σxy = 37 (c) Find the equation of the regression line between y and x.  (d) Use the equation in part (c) to predict y when x=3.5.  (e) Test whether the slope of the population regression line is positive against the default that it is zero is   Ho B₁ = 0 vs H, B₁ > 0. Use a=0.05.

Find the critical value, t, for c = 0.95 and n 16. d O A. 2.131 О В. 2.947 О с. 2.602 nts O D. 2.12O r

(5) Let p(t) denote the population of the Earth in the year t. According tothe internet, p(2017) = 7.55 billion. According to the lecture on populationgrowth, it is reasonable to assume thatdp/dt = kp − λp2with k = 0.029, λ = 2.695 × 10−12. Assuming all of this is true, answer thefollowing questions:(a) What will be the Earth’s population in 2030?(b) When “will” (or has it happened already?) the growth rate of theEarth’s population begin to decrease?(c) When did God create man? (That is: When were Adam and Evethe only two people on Earth? You will note that no major “religiousmythology” offers a figure as implausible as the one you will computefrom this model...)

14. Determine the critical value of t in the following circumstance from t-table: 1 – α = 0.95, with n = 32 (that is, P(t < t critical value)=0.95)

4 If P(A) = 0.2, P (B) = 0.4 and P(A |B)) = 0.1 Compute P(A'n B) Enter your answer with two decimal places.

A researcher has boiled her hypothesis test down to the following information. Ho: μ = 43, Ηα: μ > 43, α = 0.1 x = 43.6959, s = = 2.6794, n = = 28 Find the p-value.