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The authors of a paper studied a random sample of 353 Twitter users. For each Twitter...

The authors of a paper studied a random sample of 353 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 63 64 99 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. (Hint: See Example 12.2.)

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.

H0: p1 = p2 = p3 = p4 = p5 = 353
Ha: H0 is not true.H0: p1 = p2 = p3 = p4 = p5 = 70
Ha: H0 is not true.    H0: p1 = p2 = p3 = p4 = p5 = 0.05
Ha: H0 is not true.H0: p1 = p2 = p3 = p4 = p5 = 0.2
Ha: H0 is not true.H0: p1 = p2 = p3 = p4 = p5 = 0.5
Ha: H0 is not true.

Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)

X2=

P-value=

State the conclusion in the problem context.

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 convincing 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 not convincing 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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