Question

interesting significantly underrepresented in their number of 2) A recent analysis of the Communication Department listserv revealed an that undergraduates hypothesis: messages. The COMM population is 80% undergraduates, 16% graduate students, and 4% Faculty. An anaylsis of messages to date in 2016 revealed that 204 messages came from undergraduates, 94 from graduates, and 77 from faculty. Was the hypothesis supported? (20 Points were

Hi! I need solutions for this one. Use alpha = 0.05. Thanks!

Answer 1

Date: 25/06/2019 Answer To test the hypothesis is that the observed distribution of messages is not same as expected at 5% level of significance The null and alternative hypothesis is, expected The null hypothesis is that the observed distribution ofmessages is same as The alternative hypothesis is that the observed distribution of messages is not same as expected The chi-square test statistic for goodness-of-fit test is, First, compute frequency expected then find chi-square test statistics The expected frequency for undergraduates is, f. Npi =375 x 80% X =300

The expected frequency for graduates is, f. Npi - 375x 16% 60 The expected frequency for faculty is, f. Npi - 375 x 4% = 15 The chi-square test statistic for goodness-of-fit test is, fa (94- 60)2 (77-15) (204-300)2 60 300 15 = 306.25 -

The chi-square test statistic for goodness-of-fit test is 306.25 The chi-square critical value is, We need to find degrees of freedom for finding chi-square critical values degrees of freedom = k -1 = 3-1 -2 From the critical value table, show degrees of freedom 2 and the significance level 0.05 so the chi-square critical value is 5.991. The chi-square critical value is 5.991 Decision The conclusion is that chi-square test statistic 306.25 greater than chi-square critical value 5.991, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that the observed distribution of messages is not same as expected. The result is statistically significant.