N O 3. For each hypothesis given below, show on the graph shown the rejection region(s) after showing on the graph the critical point(s) za or za (i) Orl 1:0HS Use a 0.05 Ha: u> Ho . 4 2 2 4 Z The rejection region is
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It is given that the level of significance is 0.05.
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- A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.a) Find the marginal pmfs of X and Y b) Find the conditional pmf of X given Y = 1a=0.05, z=1.30, h a:u1=/u2 A is the positive critical value for this question, what is/are the possible critical region(s) for this hypothesis test? A. Greater than -A and smaller than A B. Greater than A or smaller than -A C. Greater than A D. None of the above E. Smaller than -A
- Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. 99%; n = 17; σ is unknown; population appears to be normally distributed. Group of answer choices tα/2 =2.921 zα/2 =2.583 zα/2 = 2.567 Neither the normal nor the t distribution applies.a=0.01, z=2.79, h a:u1>u2 A is the positive critical value for this question, what is/are the possible critical region(s) for this hypothesis test? A. Greater than A B. Greater than -A or smaller than A C. Smaller than A D. None of the above E. Greater than A or smaller than -Aa. Use the 2nd-order Runge-Kutta Method to approximate y(t) with h= 0.25 b. Use the 4th-order Runge-Kutta Method to approximate y(t) with h=0.25 c. Plot both sets {yi} obtained in (1) and (2) d. Determine the eventual population level (as t→∞) reached from initial population.
- Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. 98%; n = 47; σ = 27; population appears to be skewed. Group of answer choices zα/2 = 2.05 zα/2 =2.33 Neither the normal nor the t distribution applies. tα/2 =1.96An education researcher claims that at most 3% of working college students are employed as teachers or teaching assistants. In a random sample of 600 working college students, 5% are employed as teachers or teaching assistants. At α=0.01, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below. (a) Find the critical value(s) and identify the rejection region(s). Z0=_________ (b) Identify the critical value(s) for this test ________ A.) The rejection regions are z < ___and z > ____ B.) The rejection region is z > _______ C.) The rejection region is _____< z < _____ D.) The rejection region is z < _____ (c) Decide whether to reject or fail to reject the null hypothesis and (d) interpret the decision in the context of the original claim.Consider the null hypotheses for the following multinomial experiments. (Give your answers correct to two decimal places.) (a) Determine the critical value and critical region that would be used in the classical approach to test Ho: P(1) = P(2) = P(3) = P(4) = 0.25, with a = 0.005.X2 (b) Determine the critical value and critical region that would be used in the classical approach to test Ho: P(1) = 0.25, P(2) = 0.40, P(3) = 0.35, with a = 0.1.X2
- -Suppose we fail to reject Ho: μ ≥ 50 When the true mean is μ = 53Given a sample of size n=64 and σ =6 and with α=0.05Calculate the critical sample mean Xα , the ZX̅α , The probability of type II error βand the power of the hypothesis test P.Solution: [Write the rules/formula]Calculate X̅α :Calculate ZX̅α with the true mean μ = 53:The probability of type II error β:The power of the hypothesis test P:If you found t(60) = 1.70, one tailed, what can we conclude about this results significance? A) The t obtained value exceeds the critical value at the p < 0.05 level but not the p < 0.01 level B) The t obtained value exceeds the critical value at the p < 0.05 level and the p < 0.01 level C) The t obtained value does not exceed either the critical value at the p < 0.05 level or the p < 0.01 level D) The t obtained value exceeds the critical value at the p < 0.01 level but not the p < 0.05 levelThe critical value for t for n = 10 for a one tail test at α = 5% LOS is