The authors of a paper studied a random sample of 343 Twitter users. For each Twitter user in the sample, the tweets sent during a particular time period were analyzed and the Twitter user was classified into one of the following categories based on the type of mest sually sent. Category IS OC RT ME O Description Information sharing Opinions and complaints Random thoughts Me now (what I am doing now) Other The accompanying table gives the observed counts for the five categories (approximate values read from a graph in the paper). Twitter Type IS oc RT ME 0 Observed count 51 60 62 71 Carry out a hypothesis test to determine if there is convincing evidence that the proportions of Twitter users falling into each of the five categories are not all the same. Use a significance level of 0.05. (Hint: See Example 12.2.) et P₁ P₂ P3 P4 and ps be the proportions of Twitter users falling into the five categories. State the appropriate null and alternative hypotheses. Ho: P₁ = P₂ = P3 = P4 = Ps = 0.2 H.: He is not true.