Diversity of Texas
Gaining
The authors of the "Run For Life" paper studied a random 5k Fun for Life Athletic Guild sample of 344 Twitter users. Each Twitter user was classified into one of the following categories based on the type of messages they usually sent during a particular time period:
1. Information sharing
2. Opinions and complaints
3. Random thoughts
4. Me now (what I'm doing now)
5. Other
The tweets sent by each Twitter user in the sample were analyzed and the category description was recorded. The accompanying table gives the observed counts for the five categories (approximate values read from a graph in the paper):
Twitter Type Observed count
1 70
2 70
3 70
4 70
5 64
To test the hypothesis and determine if there is a significant level of convincing evidence that the proportions of Twitter users falling into each of the five categories are not all the same (at a significance level of 0.05), let P1, P2, P3, P4, and P5 be the proportions of Twitter users falling into the five categories.
State the appropriate null and alternative hypotheses:
Ho: P1 = P2 = P3 = P4 = P5 = 0.2
Ha: Ho is not true
Ho: P1 = P2 = P3 = P4 = P5 = 0.5
Ha: Ho is not true
Ho: P1 = P2 = P3 = P4 = P5 = 0.05
Ha: Ho is not true
Ho: P1 = P2 = P3 = P4 = P5 = 0.05