I need help writing the confidence interval?A.)  The assumed standard deviation = 0.5     Variable   N   Mean StDev SE Mean      90% CI Price         16  5.516  1.176   ...

I need help writing the confidence interval?

A.)  The assumed standard deviation = 0.5

 

 

Variable   N   Mean StDev SE Mean      90% CI

Price         16  5.516  1.176    0.125  (5.310, 5.721)

 

 

Test of mu = 5 vs > 5

Asked on by mlunar74

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

We are given `mu=5,sigma=.5,bar(x)=5.516,n=16` . We want to test at the 90% confidence level `(alpha=.1)` whether the true mean is greater than 5.

(1) `H_0:mu=5`   `H_1:mu>5`

(2) The critical point is `z_alpha=z_.1=1.28` Thus the critical region is `z>1.28`

(3) The test value is `z=(bar(x)-mu)/(sigma/sqrt(n))=(5.516-5)/(.5/sqrt(16))=4.128`

(4) The test value is in the critical region so we reject the null hypothesis

(5) There is sufficient evidence to conclude with a 90% certainty that `mu>5`

** If you meant for the standard deviation to be 1.176 then the critical region stays the same and the test value is `(5.516-5)/(1.176/sqrt(16))=1.755` which is still in the critical region.**

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If you really just want the confidence interval (no hypothesis test) then you have:

`bar(x)-z_(alpha/2)(sigma/sqrt(n))<=mu<=bar(x)+z_(alpha/2)(sigma/sqrt(n))` or

`5.516-1.64(.5/4)<=mu<=5.516+1.64(.5/4)`

`5.311<=mu<=5.721`

(Note the use of `alpha/2` )

Sources:

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