For the homework question how do I find the chi-square test-statistic for this data? You are conducting a multinomial hypothesis test for the claim that the 4 categories occur with thefollowing frequencies:Ho: PA = 0.1; PB = 0.3; pc = 0.5; pp = 0.1Complete the table.CategoryABсDObservedFrequency30384729ExpectedFrequencySquaredResidualWhat is the chi-square test-statistic for this data?x² =Report all answers accurate to three decimal places.VERY IMPORTANT NOTE: Answers are reported to 3 decimal places, but you should use all the decimalplaces to calculate the final chi-square test statistic...DO NOT use the rounded number you report in thetable.

The hypothesized proportions for the categories are:H0:pA=0.1; pB=0.3, pC=0.5, pD=0.1The observed frequencies for the categories are:CategoryObserved frequencyA30B38C47D29The total of the observed frequencies is:N=30+38+47+29=144The expected frequency for each of our categories is based on the corresponding hypothesized proportion. The expected frequencies are calculated as follows:Category; iExpected frequency; NpiA144×0.1=14.400B144×0.3=43.200C144×0.5=72.000D144×0.1=14.4Now the Chi-square test statistic is formulated as:χ2=∑i(Oi−Ei)2Ei; where, Oi: observed frequency, Ei: expected frequencyCalculation Table: CategoryObserved frequency; OiExpected frequency; Ei Squared residual; (Oi−Ei)2" data-mce-style="cursor: default;">3014.4243.36" data-mce-style="cursor: default;">3843.227.04" data-mce-style="cursor: default;">4772625" data-mce-style="cursor: default;">2914.4213.16The Chi-squared test statistics is calculated as follows:χ2=∑i(Oi−Ei)2Ei=243.3614.4+27.0443.2+62572+213.1614.4=41.00925926≈41.009The table is computed as: CategoryObserved frequencyExpected frequency Squared residualA3014.400243.360B3843.20027.040C4772.000625.000D2914.400213.160And the test statistic, χ2=41.009.