The load life X was measured (in millions of revolutions) for 80 ceramic ball be

Question

The load life X was measured (in millions of revolutions) for 80 ceramic ball bearings subjected to a 6.45kN load. A summary of the data from JMP is on the next page. 1. a) The load life needs to average more than 150 for bearings of this type. Is there sufficient evidence to justify this claim? Explain fully, showing all parts of a hypothesis test, with 0.01 significance level. b) What do the normal diagnostic plot (Q-Q plot) and Shapiro-Wilk's test indicate about distribution of X, in terms of shape, symmetry, etc.? Is a normal distribution plausible? c) Use the delta method to approximate SE(X1/3) Summary Statistics Goodness-of-Fit Test Shapiro-Wilk W Test 175.6242 86.28983 Std Dev W 0.921522 P-Value 0.0001 445.9349 10461532 10105432 49.133224 62.52666 450.14769 158.04947 CV Normal Diagnostic Plot 500 450 400 350 300 250 200 150 100 50 0.015 0.05 009 0.16 03 0.5 0.7 084 091 0.95 Normal Probability

Explanation / Answer

Solution1A:

From summary we can conclude that mean>median

load life is positively skewed

Test for Hypothesis of single mean:

State null and alternative hypothesis.

Null hypothesis

H0: mean=150

Alternative Hypothesis:

H1:mean>150

alpha=0.01

calculation of test statistic:

Given sample mean=xbar=175.6242

sample sd=86.289831

sample size=n=80

t=175.6242-175/86.289831/sqrt(80)

t=0.065

Calculation of p value

Degrees of freedom=n-1=80-1=79

alpha=0.01

P value=0.474169

p>0.01

Decsion:

p>0.01 fail to reject null hypothesis

Accept Null hypothesis

Conclusion:

there is no sufficient evidence at 1% level of significance to conclud that average more than 150

Solutionb:

From normal probablilty plot

normal probability plot is formed by

vertical axis:load life

horizontal axis :normal order statistic medians

The points on this plot form a does not form nearly linear pattern,which indicates not a normal d

there are outliers.istribution

Shapiro test:

H0:samples come form normal distribution

H1:samples do not come form normal distribution

test statistic:0.9215

p<0.01

Reject Null hypothesis

does not follow normal distribution

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