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15. Calculate the pp-value for each of the given hypothesis test scenarios below. Round pp-values to four decimal places.

Find the p-value for a left-tailed test of hypothesis for a mean when the test statistic has been calculated as -2.08. Assume the population standard deviation is known.

p-value=

Find the p-value for a right-tailed test of hypothesis for a mean when the test statistic has been calculated as 1.26. Assume the population standard deviation is known.

p-value=

Find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as 0.42.

p-value=

Find the p-value for a two-tailed test of hypothesis for a proportion when the test statistic has been calculated as -1.46.

p-value=

Let P be the transition matrix of a Markov chain with 7 states. Which one of the following statements is not always true? O p2 is the transition matrix of a Markov chain with 72 states. If O is another transition matrix of a Markov chain with 72 states, then PQ is the transition matrix of a Markov chain with 72 states. O If ) is another transition matrix of a Markov chain with 72 states, then *(P + Q) is the transition matrix of a Markov chain with 7, states. If P is invertible, then p-1 is the transition matrix of a Markov chain with 71, states.Question 20 1 pts Let P be the transition matrix of a Markov chain with n states. Which one of the following statements is not always true? If Q is another transition matrix of a Markov chain with n states, then =(P + Q) is the transition matrix of a Markov chain with n states. O P2 is the transition matrix of a Markov chain with n states. If P is invertible, then p-1 is the transition matrix of a Markov chain with n states. If Q is another transition matrix of a Markov chain with n states, then PQ is the transition matrix of a Markov chain with n states.Let Vn ~x2 and Th ~ t, for all positive integers n. (a) Find numbers a,, and b,, such that a, (V., -b, ) converges in distribution to /(0, 1) (1 point) (b) Show that T./ (n + 7") has a Beta distribution. Specify the parameters of the Beta distribution. (1 point) Hint: You should be able to do part (b) by using the Beta Gamma connection.For this question, Could you tell me how to distinguish Binomial distribrition, Exponential distribution, Beta distribution, uniform distribution Suppose you are an telephone operator of a company and your job is to answer the phones. Let the waiting time between two phone calls be T. Decide a distribution of T. O Binomial Distribution O Exponential Distribution O Beta Distribution O Uniform Distribution