10.32 The article "Positive Aspects of Caregiving" (Research on Aging (2004) 26:429-453)describes a study that assessed how caregiving to Alzheimer's patients impacted the caregiversMost people would generally think that family members who provide daily care to parents andspouses with Alzheimer's disease would tend to be negatively impacted by their role as caregiver.The study asked 1,229 caregivers to respond to the following statement: "Caregiving enabled meto develop a more positive attitude toward life." The following responses were reported:ResponseDisagreea LotDisagreea LittleAgreea Little23419.2Agreea LotNo OpinionTotalNumber% of total16613.51169.454244.11,22910013.9a. Provide a graphical display of the data that illustrates potential differences in theb. Is there significant evidence that the proportions are not equally dispersed overc. Based on the graph in part (a) and your conclusions from part (b), does provid-percentages in the five cells.the five possible responses? Use a -.05ing care to Alzheimer's patients have generally a positive or negative impact oncaregivers?

Question
Asked Mar 25, 2019
10.32 The article "Positive Aspects of Caregiving" (Research on Aging (2004) 26:429-453)
describes a study that assessed how caregiving to Alzheimer's patients impacted the caregivers
Most people would generally think that family members who provide daily care to parents and
spouses with Alzheimer's disease would tend to be negatively impacted by their role as caregiver.
The study asked 1,229 caregivers to respond to the following statement: "Caregiving enabled me
to develop a more positive attitude toward life." The following responses were reported:
Response
Disagree
a Lot
Disagree
a Little
Agree
a Little
234
19.2
Agree
a Lot
No Opinion
Total
Number
% of total
166
13.5
116
9.4
542
44.1
1,229
100
13.9
a. Provide a graphical display of the data that illustrates potential differences in the
b. Is there significant evidence that the proportions are not equally dispersed over
c. Based on the graph in part (a) and your conclusions from part (b), does provid-
percentages in the five cells.
the five possible responses? Use a -.05
ing care to Alzheimer's patients have generally a positive or negative impact on
caregivers?
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10.32 The article "Positive Aspects of Caregiving" (Research on Aging (2004) 26:429-453) describes a study that assessed how caregiving to Alzheimer's patients impacted the caregivers Most people would generally think that family members who provide daily care to parents and spouses with Alzheimer's disease would tend to be negatively impacted by their role as caregiver. The study asked 1,229 caregivers to respond to the following statement: "Caregiving enabled me to develop a more positive attitude toward life." The following responses were reported: Response Disagree a Lot Disagree a Little Agree a Little 234 19.2 Agree a Lot No Opinion Total Number % of total 166 13.5 116 9.4 542 44.1 1,229 100 13.9 a. Provide a graphical display of the data that illustrates potential differences in the b. Is there significant evidence that the proportions are not equally dispersed over c. Based on the graph in part (a) and your conclusions from part (b), does provid- percentages in the five cells. the five possible responses? Use a -.05 ing care to Alzheimer's patients have generally a positive or negative impact on caregivers?

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Expert Answer

Step 1

Part (a): Graph:

This is a categorical data, with the 5 categories representing the 5 responses to the given question. There may be several graphical displays, such as, simple bar chart, stacked bar chart, pie chart, etc.

We have provided the simple bar chart of the percentages using EXCEL. Simple enter the data responses in one column, the percentages in the next column, go to “Insert” and select the first option under “Bar Chart”. You can edit the axes titles in “Design > Chart Layouts”, by selecting the already constructed graph.

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Step 2

Part (b): Test:

Hypotheses:

The aim is to check whether the proportions are independent for the five responses and are equal.

The null hypothesis is:

H : The five proportions are independent, leading to equal proportions for all five  responses.

The alternative hypothesis is:

H : The five proportions are not independent, leading to unequal proportions for the responses.

Calculation steps:

The calculations have been done in EXCEL.

Denote Oi as the observed frequency for ith response (i =1, 2, …, 5) andEei as the expected frequency for ith response. In this case, each Ei = 0.2 (= 1/5).

Test statistic:

The formula for the test statistic is χ2 = ∑ [(OiEi)2 / Ei], summed over all i.

The Table 1 calculates [(OiEi)2 / Ei] for each i. So, the value in the first cell will be (166 – 245.8)2 / 245.8 ≈ 25.91.

The test statistic value can be calculated by adding all these cell values.

The degrees of freedom is (5 – 1) = 4.

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Step 3

Test statistic value:

The test statistic value is: 25.91 + 68.54 + 22.76 + 0.57 + 356.93 = 474.71.

Critical value:

The level of significance is α = 0.05. Therefore, the critical value will be χ20.05.

From EXCEL formula “=CHISQ.INV.RT(0.05, 4)”, the critical value χ20.05 = 9.49.

Deci...

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