The number of defects in printed circuit boards is hypothesized to have failure

Question

The number of defects in printed circuit boards is hypothesized to have failure rates as given in table I. A researcher believes that the failure rate is different than as illustrated in table 1. She collects data and the observed failure rates of the printed circuit board is given in table II. Conduct a chi-squared test to determine if the collected data provide sufficient evidence to contradict the null hypothesis at a significance level of 0.05 that p_0 = 0.472, p_1 = .354, p_2 = .133 and p_4 = .041. (Include the null hypothesis, alternative hypothesis, decision and conclusion along with the analysis)

Explanation / Answer

null hypothesis: distribution follows given proposed probability distribution

alternate hypothesis:distribution does not follows given proposed probability distribution

crtiical value =7.815

as test stat 3.4059 is less then critical value we can not reject null hypothesis. And conclude that distribution follows given proposed probability distribution

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E 0 0.472 32.000 28.32 0.48 1 0.354 15.000 21.24 1.83 2 0.133 9.000 7.98 0.13 3 0.041 4.000 2.46 0.96 1 60 60 3.4059

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