Question
An engineer examined the hardness of 36 pieces of steel created using a new process. Suppose...
An engineer examined the hardness of 36 pieces of steel created
using a new process. Suppose that the average hardness was 175 and
that the standard hardness of steel is 170 with a known standard
deviation of 10. Is there conclusive evidence that the hardness of
this new steel is greater than 170?
A) State the null and alternative hypotheses.
o H0: μ = 170, HA: μ > 170
o H0: μ = 170, HA: μ < 170
o H0: μ = 170, HA: μ ≠ 170
B) Find the test statistic.
z =
C) What is the p-value?
P-Value =
D) State your conclusion in terms of the null hypothesis. Take α =
0.05.
We fail to reject the null hypothesis. There is conclusive evidence that the mean hardness of steel is greater than 170.We reject the null hypothesis. There is not conclusive evidence that the mean hardness of steel is greater than 170. We fail to reject the null hypothesis. There is not conclusive evidence that the mean hardness of steel is greater than 170.We reject the null hypothesis. There is conclusive evidence that the mean hardness of steel is greater than 170.
Homework Answers
Answer #1
H0: μ = 170, HA: μ > 170
Test statistic = z
= (
- 
) / 
/ 
n
= (175 - 170) / 10 /
36
= 3
Test statistic = 3
P-value = 0.0013
P-value < 
Reject the null hypothesis .
There is conclusive evidence that the mean hardness of steel is greater than 170.
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