Question

A sample of 220 patients of a family medicine practice was surveyed two weeks after their doctor's visit to ask them whether the symptoms that prompted their visit improved, and whether they complied with the physician's treatment plan. The following table contains the results.

	Symptoms improved	Symptoms did not improve
Complied	100	40
Did not comply	30	50

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Is there a relationship between the two variables?

	a.	There is no relationship between the variables, because the probabilities sum up to 1.
	b.	There is a relationship between the variables, as the column percentages are not the same.
	c.	There is a relationship between the variables because the number of patients that improved and complied with the treatment plan is greater than the number that complied and did not improve.
	d.	We need additional information to determine if there is a relationship between those two variables.

Answer 1

Given table data is as below MATRIX col1 col2 TOTALS row 1 100 40 140 row 2 30 50 80 TOTALS 130 90 N = 220 ------------------------------------------------------------------ calculation formula for E table matrix E-TABLE col1 col2 row 1 row1*col1/N row1*col2/N row 2 row2*col1/N row2*col2/N ------------------------------------------------------------------ expected frequecies calculated by applying E - table matrix formulae E-TABLE col1 col2 row 1 82.7273 57.2727 row 2 47.2727 32.7273 ------------------------------------------------------------------ calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above Oi Ei Oi-Ei (Oi-Ei)^2 (Oi-Ei)^2/Ei 100 82.7273 17.2727 298.35 3.6064 40 57.2727 -17.2727 298.35 5.2092 30 47.2727 -17.2727 298.35 6.3112 50 32.7273 17.2727 298.35 9.1161 ᴪ^2 o = 24.2429 ------------------------------------------------------------------ set up null vs alternative as null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent level of significance, α = 0.05 from standard normal table, chi square value at right tailed, ᴪ^2 α/2 =3.8415 since our test is right tailed,reject Ho when ᴪ^2 o > 3.8415 we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei from the table , ᴪ^2 o = 24.2429 critical value the value of |ᴪ^2 α| at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415 we got | ᴪ^2| =24.2429 & | ᴪ^2 α | =3.8415 make decision hence value of | ᴪ^2 o | > | ᴪ^2 α| and here we reject Ho ᴪ^2 p_value =0 ANSWERS --------------- null, Ho: no relation b/w X and Y OR X and Y are independent alternative, H1: exists a relation b/w X and Y OR X and Y are dependent test statistic: 24.2429 critical value: 3.8415 p-value:0 decision: reject Ho

we have enough evidence to support the claim that there is  relationship between the two variables

option:B