A thread manufacturer was interested in how many breaks in thread occurred for f

Question

A thread manufacturer was interested in how many breaks in thread occurred for four winding speeds (slow, Normal, fast, Maximum).The number of breaks for 10000 spools was recorded.Diagnostic plots are found on the back page.

(a) Based on the plots, does it appears as though the assumptions for ANOVA are met? Explain

(2)State the null and alternative for the shapiro wilks test

(3)State the null and alternative for the Brown- Forstyhe test.

(4) The p-value for the hypothesis of equal means on this data was: 7.593x10^-16. Do you believe it is reliable? Explain

(5)The p-value for the shpiro - wilks test is: 0.0734. Interpret this P value in terms of the problem

(6)The p-value for the brown forsthe test is:0.0000304. Interpret this p value in terms of the problem

Errors vs. Group Means Normal Q-Q Plot Histogram of errors 2 2 10 0 10 e in number of breaks) 10 16 Theoretical Quantdes Group Means

Explanation / Answer

(a) Based on the plots, does it appears as though the assumptions for ANOVA are met

yes since from the dot plot the four group means are different.

From QQ plot,Significant departures from the line suggest violations of normality.

(2)State the null and alternative for the shapiro wilks test

Null hypothesis:

Data comes from normal Distribution

Alternative Hypothesis:

Data deviates from normal Distribution

Solution3:

Null hypothesis:variances of the sampled groups are the same.

alternative Hypothesis:

Atleast one of variances of the sampled groups are not the same.

Solution4:

(4) The p-value for the hypothesis of equal means on this data was: 7.593x10^-16. Do you believe it is reliable? Explain

p<0.05

Reject null hypothesis.

there is sufficient statsitical evidence at 5% level of significance to conclude that atleast one of the group(slow, Normal, fast, Maximum)means are different.

There are difference in group means.

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