4. -6 points My Notes Ask Your Teache Let X1.x2, x be a sample of observations f

Question

4. -6 points My Notes Ask Your Teache Let X1.x2, x be a sample of observations from a normal population with unknown mean and unknown standard deviation . Suppose the sample mean is x and the sample standard deviation is s. we wish to test the null hypothesis Ho:=20 against the alternative Ha:>20. Our test statistic will be T = sample yields x = 22.25 and s = 1.91. Answer the following using R code. a)If xbar-22.. 25 and s = 1.91 then what is the value of T? b) T has a t distribution. How many degrees of freedom does this distribution have? x-20 7 c) If we test at the 1% level then what is the critical value? d) What is the p-value based upon our sample? e) Do we reject the null hypothesis at the 1% level?(Y/N)? O N FA f) If we repeat a 1% level test 300 times then about how many times do we expect to commit a type() error? 9) Copy your R script for the above into the text box here.

Explanation / Answer

a)

t = (xbar - 20)/ (s /sqrt(n))

xbar = 22.5

s= 1.91

n=8

inserting the values of xbar and s,

t = 3.702

b)

the degrees of freedom is n-1

df = n-1 = 8-1 = 7

c)

alpha = 0.01

t-stat at 7 degrees of freedom at 0.01 alpha for a right tailed test can be calculated in excel as

=+T.INV(0.01,7)

-2.9979

ignoring the sign it is 2.9979

d)

p-value is t-stat of 7 degrees of freedom lesser than critical value

it can be calculated in excel as =+T.DIST.RT(3.702,7)

p-value = 0.0038

e)

since p-value is lesser than 0.01 reject null hypothesis

Hence answer is Y

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