A machine that puts corn flakes into boxes is adjusted to put an average of 14 ounces into each box, with standard deviation of
0.24 ounce. If a random sample of 12 boxes gave a sample standard deviation of 0.38 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.
Assume volume in boxes is normally distributed.
Classify the problem as one of the following: Chi-square test of independence or homogeneity, Chi-square goodness of fit, Chi-
square for testing σ² or σ.
Chi-square test of independence
Chi-square for testing σ² or σ
Chi-square goodness of fit
Chi-square test of homogeneity
(i) Give the value of the level of significance.
0.01
State the null and alternate hypotheses.
Ο Ηο: σ² = 0.0576; Η₁: σ² + 0.0576
Ο Ηο: σ² = 0.0576; Η₁: σ² < 0.0576
Ο Ηο: σ² < 0.0576; Η₁: σ² = 0.0576
Ο Ηο: σ² = 0.0576; Η₁: σ² > 0.0576
(ii) Find the sample test statistic. (Round your answer to two decimal places.)
2.02
X
(iii) Find or estimate the P-value of the sample test statistic.
P-value > 0.100
0.050 < P-value < 0.100
0.025 P-value < 0.050
0.010 < P-value < 0.025
0.005 P-value < 0.010
P-value < 0.005
(iv) Conclude the test.
Since the P-value < a, we fail to reject the null hypothesis.
Since the P-value ≥ a, we reject the null hypothesis.
Since the P-value ≥ a, we fail to reject the null hypothesis.
Since the P-value < a, we reject the null hypothesis.
(v) Interpret the conclusion in the context of the application.
At the 1% level of significance, there is insufficient evidence to conclude that the variance has increased and the
machine needs to be adjusted.
At the 1% level of significance, there is sufficient evidence to conclude that the variance has increased and the
machine needs to be adjusted.