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 I. She collects data and the observed failure rates of the printed ciruit 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 p0 = 0.472, p1 = .354, p2 = .133 and p4 = .041. (Include the null hypothesis, alternative hypothesis, decision and conclusion along with the analysis)

Table I Number of Defects Failure Rate 0 0.472 1 0.354 2 0.133 3 0.041 Table II Number of Defects Observed Frequency 0 32 1 15 2 9 3 4

Explanation / Answer

null hypothesis: number of defects follows proposed distribution

alternate hypothesis:  number of defects follows does not proposed distribution

degree of freedom =3

critical value =7.815

as above chi stat 3.4059 is less then critical value ; we can not reject null hypothesis and conclude that above follows 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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