Question

We take a look at health, this time examining the relationship between educational attainment and perceived quality of health care. Data for three groups are presented based on the Health Information National Trends Survey (HINTS) 2012 data set. HINTS is an annual survey measuring the use of cancer-related information for adults 18 years and older. QUALITYCARE is measured on a 5-point scale: 1 = excellent, 2 = very good, 3 = good, 4 = fair, and 5 = poor. Note how a lower score indicates a higher quality of care

Answer 1

ANSWER:

It can be considered as a case of anova.

The null hypothesis H_o that means of all three groups are equal

The alternative hypothesis,i.e, H₁ is that atleast one of the mean is different

Here3 samples are given, so k=3

N=18 G=38

SS_B=5.248 , between sample DF=(k-1)=2 , MS_B=2.624

SST= 15.778 , total DF=(N-1)=17, MS_T=0.928

SS_W= (SS_T-SS_B)=10.53 , within sample DF=(N-K)=15, MS_W=0.702

F-value = MS_B/MS_W=3.737

Source of variation	D.F	Sum of squares	Mean sum of squares
Between sample	2	5.248	2.624
Within sample	15	10.53	0.702
Totl	17	15.778	0.928

No mention about the significance level is done hence it can be considered as 0.05

So from the F table , F_(2,15)=3.68

Fα=3.68 and F_calc=3.737

In one way ANOVA test decision is made in such a way that if the calculated value of F, i.e F_calc , is greater that the table value , i.e Fα , we may reject the null hypothesis.

i.e if F_calc > Fα we may reject H_o .

For this question F_calc > Fα

Hence we may reject the null hypothesis.

That is the three group of people does not have same opinion on percieved quality of health care, which can be considered as an evidence of existing relationship between educatinal attainment and percived quality of health care.

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