A machine that puts corn flakes into boxes is adjusted to put anaverage of 15.1 ounces into each box, with standard deviation of0.23 ounce. If a random sample of 15 boxes gave a sample standarddeviation of 0.35 ounce, do these data support the claim that thevariance has increased and the machine needs to be brought backinto adjustment? (Use a 0.01 level of significance.)

(i) Give the value of the level of significance.


State the null and alternate hypotheses.

H₀: ?² < 0.0529;H₁: ?² = 0.0529

H₀: ?² = 0.0529;H₁: ?² ? 0.0529

    H₀:?² = 0.0529; H₁:?² < 0.0529

H₀: ?² = 0.0529;H₁: ?² > 0.0529

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


(iii) Find or estimate the P-value of the sample teststatistic.

P-value > 0.1000

.050 < P-value < 0.100

    0.025 < P-value <0.0500

.010 < P-value < 0.0250

.005 < P-value < 0.010

P-value < 0.005

(iv) Conclude the test.

Since the P-value ? ?, we fail to reject thenull hypothesis.

Since the P-value < ?, we reject the nullhypothesis.

   Since the P-value < ?, wefail to reject the null hypothesis

.Since the P-value ? ?, we reject the nullhypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is sufficient evidence toconclude that the variance has increased and the machine needs tobe adjusted.

At the 1% level of significance, there is insufficient evidenceto conclude that the variance has increased and the machine needsto be adjusted.