(a) Identify the claim and state the null and alternative hypotheses.(b) Determine the degrees of freedom, find the critical value, and identify the rejection region.(c) Calculate the test statistic. If convenient, use technology. The contingency table shows a random sample of engineering, psychology, and biology articles and if and how they were coauthored.At a= 0.05, can youconclude that the subject Coauthorshipmatter and coauthorship Coauthoredare related? Completeparts (a) through (d).Subject matterlo|EngineeringPsychology Biology464140InternationallycoauthoredNot coauthored291313394335

Given Information: Significance level α=0.05 To test the claim that the subject matter and co-authorship are related. (a) State the Hypothesis as follows: Null Hypothesis : H0 : Subject matter and co-authorship are independent i.e., They are not related. Alternative Hypothesis H1 : Subject matter and co-authorship are dependent i.e., They are related. (b) Degrees of freedom is given by the formula: df=r-1c-1=3-13-1=2×2=4 where, r is the number of rows and c is the number of columns. Using a chi square table, for a right tailed test, at 4 degrees of freedom and 0.05 significance level, critical value is 9.488 Rejection region is χ2>9.488 If the test statistic is greater than 9.488, it falls in the rejection region and we reject the null hypothesis.(c) Test statistic is given by the formula: χ2=∑iOi-Ei2Ei where, Oi is the observed frequency and Ei is the Expected frequency. Expected frequencies are calculated as follows: E=corresponding row total×corresponding column total/Grand Total Engineering Psychology Biology Total Co-authored 127×114299=48.42 127×97299=41.20 127×88299=37.38 127 Internationally Co-authored 55×114299=20.97 55×97299=17.84 55×88299=16.19 55 Not co-authored 117×114299=44.61 117×97299=37.96 117×88299=34.43 117 Total 114 97 88 299 Calculation of the test statistic: χ2=∑iOi-Ei2Ei=0.120950021+0.000970874+0.183638309+3.074911779+1.31309417+0.62854231+0.705494284+0.669167545+0.009436538=6.706206 Thus, the value of the test statistic is 6.706 Since, computed value of the test statistic is less than the critical value, we fail to reject the null hypothesis.