A researcher records whether n-272 children do or do not have asthma at age 13,

Question

A researcher records whether n-272 children do or do not have asthma at age 13, and then again records whether these same 272 individuals have asthma 7 years later. Results are shown in the following table Asthma at age 20? Asthma at age 13? Yes No Yes 85 10 No 25 152 What is the expected frequency of "asthma at 13" and "asthma at 20"? [Answer to 2 decimal places.] Submit Answer Tries 0/3 What is the expected frequency of "asthma at 13" and "no asthma at 20"? [Answer to 2 decimal places.] What is the expected frequency of "no asthma at 13" and "asthma at 20"? [Answer to 2 decimal places.] What is the expected frequency of "no asthma at 13" and "no asthma at 20"? [Answer to 2 decimai places.] To test whether "asthma at 13" is related to "asthma at 20", what is the value of chi-square test statistic? [Answer to 3 dema places.] Suppose we are testing: Submit Answer Tries 0/3 Submit Answer Tries 0/3 Submit Answer Tries 0/3 Submit Anwer Tries 0/3 Null hypothesis: "asthma at 13" and "asthma at 20" are not related against Alternative hypothesis: "asthma at 13" and "asthma at 20" are related If the p-value associated to the ch-square test-statistics is 0 and the level of significance is 5%, what will be your conclusion? Do not reject null hypothesis O Reject null hypothesis Not enough information to reach a decision Submit Answer Tries 0/3

Explanation / Answer

here as expected frequency =row total*column total/grand total

hence applying chi square test on above data:

1) expected frequency of asthama at 13 and asthama at 20= 38.42

2)expected frequency of asthama at 13 and no asthama at 20= 71.58

3)expected frequency of no asthama at 13 and asthama at 20= 56.58

4)expected frequency of no asthama at 13 and no asthama at 20= 105.42

5) test statistic chi square =145.713 ( please try 145.719 if this comes wrong and revert)

6)as p value is less than 0.05 level

reject null hypothesis

Observed OBS Yes No Total Yes 85 25 110 No 10 152 162 Total 95 177 272 Expected Ei=?row*?column/?total Yes No Total Yes 38.420 71.580 110 No 56.580 105.420 162 Total 95 177 272 chi square =(Oi-Ei)2/Ei Yes No Total Yes 56.47 30.31 86.78 No 38.35 20.581 58.93 Total 94.82 50.89 145.713

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