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The authors of a paper studied a random sample of 355 Twitter users. For each Twitter...

The authors of a paper studied a random sample of 355 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 messages they usually sent.

Category Description
IS Information sharing
OC Opinions and complaints
RT Random thoughts
ME Me now (what I am doing now)
O 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 O
Observed count 53 59 66 103 74

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.

Let p1, p2, p3, p4, and p5 be the proportions of the five message types among the population of Twitter users.

State the null and alternative hypotheses.

H0: p1 = p2 = p3 = p4 = p5 = 0.5
Ha: H0 is not true.

H0: p1 = p2 = p3 = p4 = p5 = 355
Ha: H0 is not true.   

H0: p1 = p2 = p3 = p4 = p5 = 70
Ha: H0 is not true.

H0: p1 = p2 = p3 = p4 = p5 = 0.2
Ha: H0 is not true.

H0: p1 = p2 = p3 = p4 = p5 = 0.05
Ha: H0 is not true.


Calculate the test statistic. (Round your answer to two decimal places.)
χ2 =  

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =  

What can you conclude?

Do not reject H0. There is not enough evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.

Do not reject H0. There is convincing evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.    

Reject H0. There is convincing evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.

Reject H0. There is not enough evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.

Math   Statistics-And-Probability   
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