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 l. 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 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_o = 0.472, p_1 = .354, p_2 = .133 and p4 = .041. (Include the null hypothesis, alternative hypothesis, decision and conclusion along with the analysis)

Explanation / Answer

null hypothesis: failure rate are similar as illustrated in the table

alternate hypothesis: failure rate are different from as illustrated in the table

at 0.05 level of singnificance with 3 degree of freedom ; critical value =7.8147

as chi stat 3.4059 is less then critical valuw we can not reject null hypothesis

observed Expected Chi square X Probability O E=total*p =(O-E)^2/E 0 0.4720 32.000 28.32 0.48 1 0.3540 15.000 21.24 1.83 2 0.1330 9.000 7.98 0.13 3 0.0410 4.000 2.46 0.96 1 60 60 3.4059

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