Question

Asked Mar 25, 2019

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.

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*_{0} : The five proportions are independent, leading to equal proportions for all five responses.

The alternative hypothesis is:

*H*_{1} : The five proportions are not independent, leading to unequal proportions for the responses.

**Calculation steps:**

The calculations have been done in EXCEL.

Denote *O _{i}* as the observed frequency for

**Test statistic:**

The formula for the test statistic is *χ*^{2} = ∑ [(*O _{i}* –

The Table 1 calculates [(*O _{i}* –

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

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

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 *χ*20.05.

From EXCEL formula “=CHISQ.INV.RT(0.05, 4)”, the critical value *χ*20.05 = 9.49.

**Deci...**

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