Question
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
Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of21roller bearings from the old manufacturing process showed the sample variance of diameters to be
s2=0.237.
Another random sample of28roller bearings from the new manufacturing process showed the sample variance of their diameters to be
s2=0.146.
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 estimating2or,Ftest for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.
Ftest for two variancesOne-way ANOVAChi-square test of homogeneityChi-square test of independenceChi-square for testing or estimating2orTwo-way ANOVAChi-square goodness-of-fit
(i) Give the value of the level of significance.
State the null and alternate hypotheses.
H0:12=22;H1:1222H0:12<22;H1:12=22H0:12=22;H1:12<22H0:12=22;H1:12>22
(ii) Find the sample test statistic. (Round your answer to two decimal places.)
(iii) Find theP-value of the sample test statistic.
P-value > 0.2000.100 <P-value < 0.2000.050 <P-value < 0.1000.020 <P-value < 0.0500.002 <P-value < 0.020P-value < 0.002
(iv) Conclude the test.
Since theP-value is greater than or equal to the level of significance= 0.05, we fail to reject the null hypothesis.Since theP-value is less than the level of significance= 0.05, we reject the null hypothesis.Since theP-value is less than the level of significance= 0.05, we fail to reject the null hypothesis.Since theP-value is greater than or equal to the level of significance= 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
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started