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An engineer is testing the shear strength of spot welds used on a construction site. The engineer's null hypothesis at a 5% level of signigicance, is that th mean shear strenfth of spot welds is at least 3.1 MPa. The engineer randomly selcts 15 Welds and measures the shear strength is 3.07 MPa with a sample standard deciation of 0.069 MPa. Which of the following statment is true?
a) The null hypothesis should not be rejected.
b) The null hypothesis should be rejected.
c) The alternate hypothesis should be rejected.
d) The null and alternate hypotheses are equally likely.

Sagot :

akiran007

Answer:

b) The null hypothesis should be rejected.

Explanation:

The null hypothesis is  that the mean shear strength of spot welds is at least

3.1 MPa

H0: u ≥3.1 MPa  against the claim Ha: u< 3.1 MPa

The alternate hypothesis is  that the mean shear strength of spot welds is less than 3.1 MPa.

This is one tailed test

The critical region Z(0.05) < ± 1.645

The Sample mean= x`= 3.07

The number of welds= n= 15

Standard Deviation= s= 0.069

Applying z test

z= x`-u/s/√n

z= 3.07-3.1/0.069/√15

z= -0.03/0.0178

z= -1.68

As the calculated z= -1.68  falls in the critical region Z(0.05) < ± 1.645 the null hypothesis is rejected and the alternate hypothesis is accepted that the mean shear strength of spot welds is less than 3.1 MPa

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