Category Description IS Information sharing OC Opinions and complaints RT Random thoughts ME Me now (what I am doing now) O Other Twitter Type IS OC RT ME O Observed count 51 63 62 99 71 Ho: P1 = P2 = P3 = P4 = P5 = 346 H1: Ho is not true. Ho: P1 = P2 = P3 = P4 = P5 = 0.5 H1: Ho is not true. Ho: P1 = P2 = P3 = P4 = P5 = 70 H1: Ho is not true. Ho: P1 = P2 = P3 = P4 = P5 = 0.05 H1: Ho is not true. Ho: P1 = P2 = P3 = P4 = P5 = 0.2 H1: Ho is not true. x² = 18.96 P-value = 0.001 Reject Ho. 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 Ho. 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 Ho. There is convincing evidence to conclude that the proportions of Twitter users falling into the five categories are not all the same.
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Step 1: The null hypothesis is that the proportions of Twitter users falling into each of the five categories are all the same. Show more…
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The authors of a paper studied a random sample of 349 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 51 62 62 99 75 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. a) 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.) X^2 = P-value = Q2.) The authors of a paper classified characters who were depicted smoking in movies released between a certain range of years. The smoking characters were classified according to sex and whether the character type was positive, negative, or neutral. The resulting data are summarized in the accompanying table. Assume that it is reasonable to consider this sample of smoking movie characters as representative of smoking movie characters. Do the data provide evidence of an association between sex and character type for movie characters who smoke? Use α = 0.05. Character Type Sex Positive Negative Neutral Male 256 107 131 Female 85 13 50 Calculate the test statistic. (Round your answer to two decimal places.) χ^2 = What is the P-value for the test? (Use technology to calculate the P-value. Round your answer to three decimal places.) P-value =
Ayushi S.
Suppose that a response can fall into one of k = 5 categories with probabilities p1, p2, , p5 and that n = 300 responses produced these category counts. Category 1 2 3 4 5 Observed Count 46 63 73 52 66 (a) Are the five categories equally likely to occur? How would you test this hypothesis? H0: At least one pi is different from 1 5 . Ha: p1 = p2 = p3 = p4 = p5 = 1 5 H0: p1 = p2 = p3 = p4 = p5 = 0 Ha: At least one pi is different from 0. H0: p1 = p2 = p3 = p4 = p5 = 1 5 Ha: At least one pi is different from 1 5 . H0: At least one pi is different from 0. Ha: p1 = p2 = p3 = p4 = p5 = 0 H0: p1 = p2 = p3 = p4 = p5 = 1 Ha: At least one pi is different from 1. (b) If you were to test this hypothesis using the chi-square statistic, how many degrees of freedom would the test have? ______ degrees of freedom (c) Find the critical value of ?2 that defines the rejection region with ? = 0.05. (Round your answer to three decimal places.) ?2 0.05 = (d) Calculate the observed value of the test statistic. ?^2 = (e) Conduct the test and state your conclusions. There is sufficient evidence to indicate that at least one category is more likely to occur than the others. There is sufficient evidence to indicate that there is not at least one category more likely to occur than the others. There is insufficient evidence to indicate that at least one category is more likely to occur than the others. There is insufficient evidence to indicate that there is not at least one category more likely to occur than the others.
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