A machine that puts corn flakes into boxes is adjusted to put an average of 15.7 ounces into each box, with standard deviation of 0.24 ounce. If a random sample of 17 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.)
(i) Give the value of the level of significance.
State the null and alternate hypotheses.
H0: σ2 < 0.0576; H1: σ2 = 0.0576 H0: σ2 = 0.0576; H1: σ2 < 0.0576 H0: σ2 = 0.0576; H1: σ2 ≠ 0.0576 H0: σ2 = 0.0576; H1: σ2 > 0.0576
(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.
To test against
Here
sample variance
and sample size n = 17
The test statistic can be written as
which under H0 follows a chi square distribution with n-1 df.
We reject H0 at 1% level of significance if P-value < 0.01
Now,
The value of the test statistic =
and p-value =
iii) Here,
p-value < 0.005,
iv) Since the P-value < α = 0.01, 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
Get Answers For Free
Most questions answered within 1 hours.