In: Statistics and Probability
A factory supplies parts for motorcycles. It produces a cylindrical engine part that is supposed to have a diameter of 6 centimetres. The factory’s quality control manager suspects that the machine producing the engine part is not working properly and that the mean diameter being produced is less than the correct size. To test if this belief is correct, a random sample of 40 parts is tested and measured. The sample mean diameter was found to be 5.9 cm. Assume that diameter size of the engine part is normally distributed with a population standard deviation of 0.26 cm.
to replace the machine? Why?
the conclusion you made in part a). Briefly explain your selection.
a)Ho : µ = 6
Ha : µ < 6
(Left tail test)
Level of Significance , α =
0.03
population std dev , σ =
0.2600
Sample Size , n = 40
Sample Mean, x̅ = 5.9000
' ' '
critical z value, z* = -1.8808 [Excel formula =NORMSINV(α/no. of tails) ]
rejecction region :
|test stat| > |1.8808|
Standard Error , SE = σ/√n = 0.2600 / √
40 = 0.0411
Z-test statistic= (x̅ - µ )/SE = (
5.900 - 6 ) /
0.0411 = -2.43
Decision: |test stat| > |critical value |
, Reject null hypothesis
.............
b)
p-Value = 0.0075 [
Excel formula =NORMSDIST(z) ]
Decision: p-value<α, Reject null hypothesis
..........
c)
the machine producing the engine part is not working properly and that the mean diameter being produced is less than the correct size
.............
d)
type I errro is there
....................
THANKS
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