Question

A machine that puts corn flakes into boxes is adjusted to put an average of 15.4...

A machine that puts corn flakes into boxes is adjusted to put an average of 15.4 ounces into each box, with standard deviation of 0.22 ounce. If a random sample of 17 boxes gave a sample standard deviation of 0.33 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 = 0.0484; H1: σ2 > 0.0484

H0: σ2 = 0.0484; H1: σ2 < 0.0484    

H0: σ2 = 0.0484; H1: σ2 ≠ 0.0484

H0: σ2 < 0.0484; H1: σ2 = 0.0484


(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.   

Homework Answers

Answer #1

given,

significance level,

Degree of freedom=17-1=16

Critical Value are given

Test staticstics

Decision making

There is enough evidence to support the calim. that standard the variance has increased and the machine needs to be brought back into adjustmen.

..........................

H0: σ2 = 0.0484; H1: σ2 > 0.0484

test statistics = 36

P-value < 0.005

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

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

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A machine that puts corn flakes into boxes is adjusted to put an average of 15.8...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.8 ounces into each box, with standard deviation of 0.22 ounce. If a random sample of 14 boxes gave a sample standard deviation of 0.36 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...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.7...
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...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.5...
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...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.1...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.1 ounces into each box, with standard deviation of 0.26 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...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.4...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.4 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. State the null...
A machine that puts corn flakes into boxes is adjusted to put an average of 15...
A machine that puts corn flakes into boxes is adjusted to put an average of 15 ounces into each box, with standard deviation of 0.24 ounce. If a random sample of 13 boxes gave a sample standard deviation of 0.36 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...
A machine that puts corn flakes into boxes is adjusted to put an average of 15.6...
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 0.22 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.) (ii) Find the sample test statistic. (Round your answer to two decimal...
A transect is an archaeological study area that is 1/5 mile wide and 1 mile long....
A transect is an archaeological study area that is 1/5 mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance σ2 = 42.3. In a different section of Chaco Canyon, a random sample of 24 transects gave a sample variance s2 = 49.7 for...
Let x represent the average annual salary of college and university professors (in thousands of dollars)...
Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ2 = 47.1. However, a random sample of 18 colleges and universities in Kansas showed that x has a sample variance s2 = 78.4. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is...
Let x represent the number of mountain climbers killed each year. The long-term variance of x...
Let x represent the number of mountain climbers killed each year. The long-term variance of x is approximately σ2 = 136.2. Suppose that for the past 11 years, the variance has been s2 = 107.1. Use a 1% level of significance to test the claim that the recent variance for number of mountain-climber deaths is less than 136.2. Find a 90% confidence interval for the population variance. (a) What is the level of significance? State the null and alternate hypotheses....