A machine that puts corn flakes into boxes is adjusted to put an average

of 15.6 ounces into each box, with standard deviation of 0.27 ounce. If a random sample of 17 boxes gave a sample standard deviation of 0.39 ounce, do these data support the claim that the variance has increased and the machine needs to be brought back into adjustment? (Use a 0.01 level of significance.)
(i) Give the value of the level of significance.

State the null and alternate hypotheses.
a.H0: σ2 = 0.0729; H1: σ2 > 0.0729
b.H0: σ2 = 0.0729; H1: σ2 ≠ 0.0729
c.H0: σ2 < 0.0729; H1: σ2 = 0.0729
d.H0: σ2 = 0.0729; H1: σ2 < 0.0729

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

(iii) Find or estimate the P-value of the sample test statistic.
a.P-value > 0.100
b.0.050 < P-value < 0.100
c.0.025 < P-value < 0.050
d.0.010 < P-value < 0.025
e.0.005 < P-value < 0.010
f.P-value < 0.005

(iv) Conclude the test.
a.Since the P-value ≥ α, we fail to reject the null hypothesis.
b.Since the P-value < α, we reject the null hypothesis.
c.Since the P-value < α, we fail to reject the null hypothesis.
d.Since the P-value ≥ α, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.
a.At the 1% level of significance, there is sufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.
b.At the 1% level of significance, there is insufficient evidence to conclude that the variance has increased and the machine needs to be adjusted.

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