Question

The authors of a paper studied a random sample of 351 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	60	66	99	73

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

α = 0.05.

(Hint: See Example 14.3.)

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 = 0.5
H_a: H₀ is not true. H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 351
H_a: H₀ is not true.     H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.2
H_a: H₀ is not true. H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 70
H_a: H₀ is not true. H₀: p₁ = p₂ = p₃ = p₄ = p₅ = 0.05
H_a: 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 not 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.     Reject H₀. There is 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 convincing evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.

Answer 1