Question

In: Statistics and Probability

Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in...

Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 21 roller bearings from the old manufacturing process showed the sample variance of diameters to be

s2 = 0.234.

Another random sample of 27 roller bearings from the new manufacturing process showed the sample variance of their diameters to be

s2 = 0.125.

Use a 5% level of significance to test the claim that there is a difference (either way) in the population variances between the old and new manufacturing processes.

Classify the problem as being a Chi-square test of independence or homogeneity, Chi-square goodness-of-fit, Chi-square for testing or estimating σ2 or σ, F test for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.

Two-way ANOVA F test for two variances     Chi-square for testing or estimating σ2 or σ One-way ANOVA Chi-square test of homogeneity Chi-square goodness-of-fit Chi-square test of independence

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


State the null and alternate hypotheses.

H0: σ12 = σ22; H1: σ12 > σ22H0: σ12 = σ22; H1: σ12σ22     H0: σ12 < σ22; H1: σ12 = σ22H0: σ12 = σ22; H1: σ12 < σ22


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


(iii) Find the P-value of the sample test statistic.

P-value > 0.200 0.100 < P-value < 0.200     0.050 < P-value < 0.100 0.020 < P-value < 0.050 0.002 < P-value < 0.020 P-value < 0.002


(iv) Conclude the test.

Since the P-value is greater than or equal to the level of significance α = 0.05, we fail to reject the null hypothesis. Since the P-value is less than the level of significance α = 0.05, we reject the null hypothesis.     Since the P-value is less than the level of significance α = 0.05, we fail to reject the null hypothesis. Since the P-value is greater than or equal to the level of significance α = 0.05, we reject the null hypothesis.


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

At the 5% level of significance, there is insufficient evidence to show that the variance for the new manufacturing process is different. At the 5% level of significance, there is sufficient evidence to show that the variance for the new manufacturing process is not different.     At the 5% level of significance, there is insufficient evidence to show that the variance for the new manufacturing process is not different. At the 5% level of significance, there is sufficient evidence to show that the variance for the new manufacturing process is different.

Solutions

Expert Solution



Related Solutions

Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in...
Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 26 roller bearings from the old manufacturing process showed the sample variance of diameters to be s2 = 0.232. Another random sample of 29 roller bearings from the new manufacturing process showed the sample variance of their diameters to be s2 = 0.13. Use a 5% level of significance to test the claim that there is...
Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in...
Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 21 roller bearings from the old manufacturing process showed the sample variance of diameters to be s2 = 0.214. Another random sample of 29 roller bearings from the new manufacturing process showed the sample variance of their diameters to be s2 = 0.115. Use a 5% level of significance to test the claim that there is...
Two possible routes for a power line are under study. In both cases, the power line...
Two possible routes for a power line are under study. In both cases, the power line will last 15 years, have no salvage value, have annual property taxes of 2% of first cost, and have a yearly power loss of $500/km. Around the lake Under the lake Length 16 km 6 km First cost $8800/km $24,000 /km Maintenance $175/km/yr $325 /km/yr If 9% interest is used, FIND 1. EUAC (Under) (round to nearest $100)   2.  EUAC (Around)  (round to nearest $100)   3....
Q1. Roller bearings are subject to fatigue failure caused by large contact loads. The problem of...
Q1. Roller bearings are subject to fatigue failure caused by large contact loads. The problem of finding the location of the maximum stress along the x axis can be shown to be equivalent to maximizing the function: = + x With the aid of the secant method, use xo=0.98 and x1=0.7 to determine to within 10-5 the value of x that maximizes f(x). Q 2. In an LRC series circuit, the impressed voltage E(t) and the charge q(t) on the...
precision manufacturing: a process manufactures ball bearings with diameters that are normally distributed with mean 25.0...
precision manufacturing: a process manufactures ball bearings with diameters that are normally distributed with mean 25.0 millimeters and standard deviation 0.07 millimeter. (a) find the 60th percentile of the diameters. (b) find the 67th percentile of the diameters. (c) a hole is to be designed so that 2% of the ball bearings will fit through it. the bearings that fit through the hole will be melted down and remade. what should the diameter of the hole be? (d)between what 2...
Part variability is critical in the manufacturing of ball bearings. Large variances in the size of...
Part variability is critical in the manufacturing of ball bearings. Large variances in the size of the ball bearings cause bearing failure and rapid wearout. Production standards call for a maximum variance of .0001 when the bearing sizes are measured in inches. A sample of 15 bearings shows a sample standard deviation of .014 inches. Use a = .10 to determine whether the sample indicates that the maximum acceptable variance is being exceeded. Compute the 90% confidence interval estimate of...
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball...
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below. Process A Process B   Mean 0.002mm      0.0026mm        Standard Deviation 0.0001mm      0.00012mm        Sample Size 25      12      The researcher is interested in...
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball...
A national manufacturer of ball bearings is experimenting with two different processes for producing precision ball bearings. It is important that the diameters be as close as possible to an industry standard. The output from each process is sampled and the average error from the industry standard is calculated. The results are presented below. Process A Process B   Mean 0.002mm      0.0026mm        Standard Deviation 0.0001mm      0.00012mm        Sample Size 25      12      The researcher is interested in...
The Acme Company manufactures large capacity Flash drives using two different manufacturing processes. The company is...
The Acme Company manufactures large capacity Flash drives using two different manufacturing processes. The company is interested in determining if there is a significant difference in the average manufacturing time of the two processes. For Process #1, a sample of 28 items shows a sample mean of 9 minutes and a sample standard deviation of 3.5 minutes. For Process #2, a sample of 23 items shows a sample mean of 13 minutes and a sample standard deviation of 4.5 minutes....
A company is manufacturing building bricks and fire bricks. Both production require two processes. Brick forming...
A company is manufacturing building bricks and fire bricks. Both production require two processes. Brick forming and Heat treatment. The requirements for the two bricks are: Building Bricks Fire Bricks Forming per 100 bricks 3 hours 2 hours Heating treatment per 100 bricks 2 hours 5 hours Total cost of the two departments in one months were: Forming $ 21 200 Heat treatment $ 48 800 Units produced during the month was: 130 000 70 000 Require: Prepare statement of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT