The authors of a paper studied a random sample of 350 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 50 61 64 102 73

Required:
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.

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danialamin danialamin · Answer 1 · 2021-04-28T10:32:54+02:00

Answer:

The null hypothesis is rejected.

Step-by-step explanation:

Assuming the proportions in each of the categories is the same which is 1/5 = 0.20.

H0: p1 = p2 = p3 = p4 = p5 = 0.2

Ha: H0 is not true.

The table is as below:

Twitter Type: Observed Count p E=350*p (O-E)^2/E

IS 50 0.2 70 5.7143

OC 61 0.2 70 1.1571

RT 64 0.2 70 0.5143

ME 102 0.2 70 14.6285

O 73 0.2 70 0.1286

-----------------------------------------------------------------------------------------------

Total 22.1428

The test statistic [tex]\chi^2[/tex] is 22.1421

The degree of freedom d is n-1=5-1 =4

The corresponding p-value from the chi-squared table is .000188.

As this value is less than the p-value for the H0 thus we reject the null hypothesis.