Suppose a chiesquared goodness of t test has been carried out to test whether the proportion of frequency of WhatsApp usage among social media users is distributed as expected. That is, the following hypotheses have been tested: H.) :"here is no significant difference between the observed and expected distribution of proportions of WhatsApp usage frequency of social media users. versus H1 :"here is a significant difference between the observed and expected distribution of proportions of WhatsApp usage frequency of social media users. The below table shows the results of a survey based on n : 484 respondents, as well as the expected percentages: \"35 Observed frequency Observed percentage Expected percentage High 27 89% 25. 49% Medium 150 30.99% 28.39% Low 56 11.57% 15.17% Never 143 29.55% 30.95% The results of the hypothesis test are as follows: Chisquared test for given probabilities data: obs.freq Xsquared = 6.6929, df = 3, pvalue = 0.08236 Furthermore. the expected counts have been calculated to be: [1] 123.3716 137.4076 73.4228 149.7980 Answer the following questions, rounding your answers to four decimal places where relevant. Assume a signicance level of or : 0.05. 1. Based on the above information. have the assumptions been met for this test? ('3 marks) : NOTE: Regardless of your answer above. when answering the following questions, assume that the assumptions have been met. 2. The test statistic is equal to (I mark): 1 3. The degrees of freedom is equal to {i mark): 4. The pvalue is equal to . Therefore, we 1 reject Hg . This means that there : sufcient evidence to support that the distribution of proportions is significantly different from what was expected. ('3 marks) The forlowrng question r's nor refs-red to the previous questions or the output provided above. 5. Suppose a chisquared test of independence is to be carried out. The total sample size is 100. The first variable of interest is a categorical variable with r = 12 categories. The second variable of interest is a categorical variable with c = 13 categories. For this study, what will be the degrees of freedom? (2 marks) Suppose a study is being carried out to determine whether a particular medical intervention has made a difference in the proportion of premature births. To determine whether the intervention made a significant difference, 60 mothers were assigned to the control group (no intervention) and 60 mothers were assigned to the intervention group, and for each birth, it was recorded whether or not the birth was premature. The number of premature births in each group was as follows: . In the control group, there were 13 premature births . In the intervention group, there were 6 premature births. To test whether the proportion of premature births was different between groups, the following hypotheses have been tested: Ho : P1 = P2 versus H1 : P1 # P2, where: . p1 denotes the proportion of premature births where the intervention has not been implemented . p2 denotes the proportion of premature births where the intervention has been implemented. Assume a significance level of a = 0.05. 1. Based on the above information, have the two-sample test of proportion conditions been met? (3 marks) NOTE: Regardless of your answer above, when answering the following questions, assume that the two-sample test of proportion conditions have been met. The results of the hypothesis test are as follows: 2-sample test for equality of proportions with continuity correction data: c(x1, x2) out of c(n, n) X-squared = 2.2512, df = 1, p-value = 0. 1335 alternative hypothesis: two. sided 95 percent confidence interval: -0. 02895168 0. 26228502 sample estimates : prop 1 prop 2 0. 2166667 0. 1000000 Answer the following questions, rounding your answers to four decimal places where relevant. 2. The estimate for p1 is p1 = Remember to provide your answer as a proportion and not a percentage). We are 95% confident that the difference in proportion between groups is within the interval and (Make sure you put the LOWER limit in the first box, and the UPPER limit in the second box.) (3 marks) 3. The p-value is equal to Therefore, we reject Ho Further supporting this conclusion is the fact that the 95% confidence interval include (4 marks)