may I have help with question 2 please. Thank you Question 2. i) suppose Y of (a

Question

may I have help with question 2 please. Thank you

Question 2. i) suppose Y of (a) What is the distribution use slide 14 fron week 4, part 2 of the theorem (b) Compute P(Y r) using table 4 of the exam statistical tables on bladdboard. If you don't know how to use that table, ask in yont surgery soselon ii) The rest of this question is about a hypothesis test using an indi random sample X,.... Xin of size n 16 fron a N(u, 4) bution. The null hypothesis is Ha 1 and the alternative is H i u 1. The significance level is a 3005. The test statistic T is (a) If Ho were true, what would the distribution of T be? (b) Write down the number to such that if the oteerved value t T ts we will reject Ho, and if t to we will not reject Ho the critical talue). (c) The true value 3. Given that, what is the distribution of T? probability (d) What is the P (T 1.64)1 given that H- min hypothesis, given that (e) What is the probability that this test rejects the

Explanation / Answer

2)a) Y -N(2,2^2)

Z = (X -mu)/sd

Z =(X-2)/2 - N(0,1)

b)P(Y>r)

P(Z> (r-2)/2)

with given r , we can find the required probability from standard normal table.

ii) T follows N(0,1)   

b)t-critical = 1.64

c) if mu is 3,

as ((X- -3)/(2/sqrt(16) ) -N(0,1)

T follows N(2,1)

d)P(T>1.64)

P((X- -1)/(2/sqrt(16) > 1.64)

P((X- -1) > 1.64 /2)

P(((X- -3) > -1.18)

P(Z>-1.18/(2/sqrt(16))

=P(Z> -2.36)

=0.9909

e) same as d) part

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