The authors of a paper studied a random sample of 351 Twitterusers. For each Twitter user in the sample, the tweets sent duringa particular time period were analyzed and the Twitter user wasclassified into one of the following categories based on the typeof 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 fivecategories (approximate values read from a graph in the paper).

Twitter Type	IS	OC	RT	ME	O
Observed count	53	60	66	99	73

Carry out a hypothesis test to determine if there is convincingevidence that the proportions of Twitter users falling into each ofthe five categories are not all the same. Use a significance levelof

? = 0.05.

(Hint: See Example 14.3.)

Let p₁, p₂,p₃, p₄, andp₅ be the proportions of Twitter users fallinginto the five categories.

State the appropriate null and alternative hypotheses.

H₀: p₁ =p₂ = p₃ =p₄ = p₅ = 0.5
H_a: H₀ is nottrue. H₀: p₁ =p₂ = p₃ =p₄ = p₅ = 351
H_a: H₀ is nottrue.     H₀:p₁ = p₂ =p₃ = p₄ =p₅ = 0.2
H_a: H₀ is nottrue. H₀: p₁ =p₂ = p₃ =p₄ = p₅ = 70
H_a: H₀ is nottrue. H₀: p₁ =p₂ = p₃ =p₄ = p₅ = 0.05
H_a: H₀ is nottrue.

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

X² = P-value =

State the conclusion in the problem context.

Do not reject H₀. There is not convincingevidence to conclude that the proportions of Twitter users fallinginto the five categories are not all the same. RejectH₀. There is not convincing evidence toconclude that the proportions of Twitter users falling into thefive categories are not all the same.    Reject H₀. There is convincing evidence toconclude that the proportions of Twitter users falling into thefive categories are not all the same. Do not rejectH₀. There is convincing evidence to concludethat the proportions of Twitter users falling into the fivecategories are not all the same.