A company produces metal pipes of a standard length, and claims that the standard deviation of the length is at most 1.2 cm. One of its clients decides to test this claim by taking a sample of 25 pipes and checking their lengths. They found that the standard deviation of the sample is 1.5 cm. Use a = 0.05 as the level of significance. Test the following hypotheses: H0:  σ=1.2 vs. H1: σ≠1.2 Equivalently, we have the hypotheses:

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A company produces metal pipes of a standard length, and claims that the standard deviation of the length is at most 1.2 cm. One of its clients decides to test this claim by taking a sample of 25 pipes and checking their lengths. They found that the standard deviation of the sample is 1.5 cm. Use a = 0.05 as the level of significance.

Test the following hypotheses:

H0:  σ=1.2 vs. H1: σ≠1.2

Equivalently, we have the hypotheses:

H0:  σ=1.4 vs. H1: σ≠1.4

Answer the following questions:

The rejection region is of the form [0,a] U [b,∞).

What is the value of a and b? (Write in 3 decimal places)

Does the outcome of the test reject or do not reject the null hypothesis? 

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