tpx Kronos Workforce C G Google EXC-Moving Its Im Other bookman value: 2.42 poin
ID: 423720 • Letter: T
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tpx Kronos Workforce C G Google EXC-Moving Its Im Other bookman value: 2.42 points A television station wishes to study the relationship between viewership of ts 11 pm. news pr viewer age (18 years or less, 19 to 35, 36 to 54, 55 or older) A sample of 250 television viewers in each age group is randomly selected, and the number who watch the station's 11 p.m. news is found for each sample. The results are given in the table below Age Group Watch 11 p m. News? Yes No Total or less 49 201 250 9 to 35 52 198 250 36 to 54 67 183 250 55 or OlderTotal 247 753 1000 79 (a) Let p1. P2. P3. and p4 be the proportions of all viewers in each age group who watch the station's 11 p.m. news. If these proportions are equal, then whether a viewer watches the station's 11 p m. news is independent of the viewers age group. Therefore, we can test the null hypothesis Ho that p1. P2. Ps. and p4 are equal by carrying out a chi-square test for independence. Perform this test by setting a 05 (Round your answer to 3 decimal places.) so (Click to select)Ho independence (b) Compute a 95 percent confidence interval for the difference between py and pa (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.) 95% Clu References eBook & Resources WorksheetExplanation / Answer
The solution to this problem takes four steps:
(1) state the hypotheses,
(2) formulate an analysis plan,
(3) analyze sample data
(4) interpret results.
We work through those steps below:
DF = (r - 1) * (c - 1) = (2 - 1) * (4 - 1) = 3
Er,c = (nr * nc) / n
E1,1 = (247 * 250) / 1000 = 61.75
E1,2 = (247 * 250) / 1000 = 61.75
E1,3 = (247 * 250) / 1000 = 61.75
E1,4 = (247 * 250) / 1000 = 61.75
E2,1 = (753 * 250) / 1000 = 188.25
E2,2 = (753 * 250) / 1000 = 188.25
E2,3 = (753 * 250) / 1000 = 188.25
E2,4 = (753 * 250) / 1000 = 188.25
?2 = ? [ (Or,c - Er,c)2 / Er,c ]
?2 = (49 – 61.75)2/61.75 + (52 – 61.75)2/61.75 + (67 – 61.75)2/61.75 + (79 – 61.75)2/61.75
+(188.2 - 201)2/188.25 +188.2 - 201)2/188.25 + (188.2 - 201)2/188.25 + (188.2 - 201)2/188.25
?2 = 15.835
where DF is the degrees of freedom, r is the number of levels of viewership, c is the number of levels of the age groups, nr is the number of observations from level r of viewership, nc is the number of observations from level c of age group, n is the number of observations in the sample, Er,c is the expected frequency count when viewership is level r and age group is level c, and Or,c is the observed frequency count when viewership is level r age group is level c.
The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 15.835.
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