Question

1. Answer to following with "True" or "False". Explain your answers briefly. (if false, explain what happen instead also) (a) Suppose that we observe a random variable Y that depend on another observed value x, through the relationYo+By+ewhere Bo,ßı and x are (b) We can reduce a by pushing the critical regions further into the tails of the (c) Decrease in the probability of the type II error always results in an increase in constants ande N(0,1). Then Y N(O,(Po+Bix)-) distribution the probability of the type I error, provided that the sample size n does not change. (d) p-value is equal to the probability of null hypothesis is false. (e) The p-value for a two-sided test is always twice the p-value for the associated right-sided test. (g) X 2 is an unbiased estimator for μ (h) Consider the following pdf, 2 r3 0 otherwise then E(X) = 2 (j) "The mean will fall within the confidence interval 95% of the time" is a correct interpretation about the 95% confidence interval of μ

Answer 1

a)

false

$Y = N(\beta_0+ \beta_1x ,\sigma ^2)$

b)

true

d)

true

A p-value is a conditional probability—given the null hypothesis is true, it’s the probability of getting a test statistic as extreme or more extreme than the calculated test statistic.

e) false

only true when distribution is symmetric like t-test, z-test

and not true like Chi-square test and F-test

f)

false

g)False

not necessary true

Please post c), h),i) and j) part again

We have to solve 4 parts only ,I solved 6 parts

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