Pad 3:56 PM 8. How often do users of a certain social media post on the site? Th
ID: 3206180 • Letter: P
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Pad 3:56 PM 8. How often do users of a certain social media post on the site? The accompanying table represents the frequency of posting for a sample of 943 respondent Print classified according to their age groups. At the 0.05 level of significance, is there evidence of a relationship between frequency of posting and age group? 4 Click the icon to view the table. State the null and alternative hypotheses to test. Ho: (1) Calculate the test statistic. (Round to two decimal places as needed.) XSTAT Determine the p-value. (Round to three decimal places as needed.) p value Make a conclusion for this test. (3) Ho. There is (4) evidence of a relationship between frequency of posts and age group 4: Type of favorite music classified by age group FREQUENCY AGE 18-22 23-35 36-49 50-64 65 and over Tota Several times a 20 20 12 56 day About once a 27 36 15 82 day 3-5 days per 35 48 30 121 week 1-2 days per 31 20 162 67 38 week. Every few weeks 19 65 49 28 167 Less often 15 57 55 61 20 208 Never 15 41 65 22 147 186 Tota 151 308 58 943 240Explanation / Answer
8. 1. To test whether frequency of posting and age groups are related, perform Chi-sqaure test of independence.
H0: there is no relationship between frequency of posts and age group.
pi1=pi2=pi3=pi4=pi5=pi6=pi7
2. H1:there is relationship between frequency of posts and age groups.
Not all pij are equal (where, j=1,2,...,7)
The test statistic is as follows:
X^2=sigma(fo-fe)^2/fe
=233.952
3. p value for 24 df [df=(row-1)(column-1)=(7-1)(5-1)=24] is 0.000.
4. Per rule, reject H0, if p value is less than 0.05. Here, p value is less than 0.05, therefore, reject H0.
There is sufficient evidence of relationship between frequency of posts and age group.
Observed frequency, fo Expected frequency, fe=[(row marginal*column marginal)/Total] (fo-fe)^2/fe 20 8.97 [(56*151)/943] 13.575 20 18.29 0.160 12 14.25 0.356 3 11.05 5.860 1 3.44 1.735 27 13.13 14.650 36 26.78 3.172 15 20.87 1.651 3 16.17 10.730 1 5.04 3.242 35 19.38 12.6 48 39.52 1.819 30 30.80 0.021 6 23.87 13.375 2 7.44 3.980 31 25.94 0.987 67 52.91 3.751 38 41.23 0.253 20 31.95 4.472 6 9.96 1.577 19 26.74 2.241 65 54.55 2.004 49 42.50 0.993 28 32.94 0.741 6 10.27 1.776 15 33.31 10.062 57 67.94 1.761 55 52.94 0.080 61 41.03 9.724 20 12.79 4.060 4 23.54 16.218 15 48.01 22.699 41 37.41 0.344 65 28.99 44.711 22 9.04 18.573X^2=sigma(fo-fe)^2/fe
=233.952
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