Question

A machine that puts corn flakes into boxes is adjusted to put an average of 15.5 ounces into each box, with standard deviation of 0.21 ounce. If a random sample of 12 boxes gave a sample standard deviation of 0.37 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.
0.01

State the null and alternate hypotheses.

H₀: σ² = 0.0441; H₁: σ² ≠ 0.0441

H₀: σ² < 0.0441; H₁: σ² = 0.0441     

H₀: σ² = 0.0441; H₁: σ² > 0.0441

H₀: σ² = 0.0441; H₁: σ² < 0.0441

(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.

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 ≥ α, we fail to reject the null hypothesis.

Since the P-value < α, we reject the null hypothesis.     

Since the P-value < α, we fail to reject the null hypothesis.

Since the P-value ≥ α, we reject the null hypothesis.

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

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

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

Answer 1

The statistical software output for this problem is :

(i)

H₀: σ² = 0.0441; H₁: σ² > 0.0441

(ii)

sample test statistic = 34.15

(iii)

P-value < 0.005

(iv)

Since the P-value < α, we reject the null hypothesis.     

(v)

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