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Sagot :
Answer:
a) H0: μ= 16 against the claim Ha: μ≠ 16
b) H0 will be rejected if it does not lie in the interval [15.934; 16.065 ]
c) 0.8531
Step-by-step explanation:
a) The null and alternate hypothesis are
H0: μ= 16 against the claim Ha: μ≠ 16
The test chosen is two sided because the cans have more or less content than 16 oz.
b) Here n = 9 , σ= 0.1 and α 0.05 and z∝/2 = ± 1.96
z∝/2 = x − µ/ σ/√n
z ∝/2= x-16/0.0333
± 1.96 *0.33= x-16
± 0.0653= x- 16
or x= 16± 0.0653
x= 15.934; 16.065
H0 will be rejected if it does not lie in the interval [15.934; 16.065 ]
c) The probability can be computed by transforming x into z
z= x-µ/ σ/√n
z= 15.934-16.1 /0.1/√9
z= [−4.95]
z2= x-µ/ σ/√n
z= 16.065-16.1 /0.1/√9
z2=[ −1.05]
P (15.934<x< 16.065 )= P (−4.95, −1.05)
=P ( z < −4.95 ) + P ( z > −1.05)
= 0+ 0.3531+0.5
= 0.8531
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