10 A scientist is researching dietary fat intake and cholesterol level. A random sample of 60 people is selected and their dietary fat intakes and cholesterol levels are measured. Dietary fat intakes are classified as low, medium and high, and cholesterol levels are classified as normal and high.
The scientist decides to carry out a chi-squared test to investigate whether there is any association between dietary fat intake and cholesterol level. Tables \(\mathbf { 1 0 . 1 }\) and \(\mathbf { 1 0 . 2 }\) show the data and some of the expected frequencies for the test.
\begin{table}[h]
| \multirow{2}{*}{} | Dietary fat intake | |
| | Low | Medium | High | Total |
| \multirow{2}{*}{Cholesterol level} | Normal | 9 | 18 | 5 | 32 |
| High | 3 | 13 | 12 | 28 |
| Total | 12 | 31 | 17 | 60 |
\captionsetup{labelformat=empty}
\caption{Table 10.1}
\end{table}
\begin{table}[h]
| Expected frequency | Dietary fat intake |
| \cline { 3 - 5 } | Low | Medium | High | |
| \multirow{2}{*}{} | Normal | | | 9.0667 |
| \cline { 2 - 5 } | High | | | 7.9333 |
\captionsetup{labelformat=empty}
\caption{Table 10.2}
\end{table}
- Complete the table of expected frequencies in the Printed Answer Booklet.
- Determine the contribution to the chi-squared test statistic for people with normal cholesterol level and high dietary fat intake, giving your answer to \(\mathbf { 4 }\) decimal places.
The contributions to the chi-squared test statistic for the remaining categories are shown in Table 10.3.
\begin{table}[h]
| Dietary fat intake | | \cline { 2 - 5 } | Low | Medium | High | | | \multirow{2}{*}{} | Normal | 1.0563 | 0.1301 | | | \cline { 2 - 5 } | High | 1.2071 | 0.1487 | 2.0846 |
\captionsetup{labelformat=empty}
\caption{Table 10.3}
\end{table}- In this question you must show detailed reasoning.
Carry out the test at the 5\% significance level.
- For each level of dietary fat intake, give a brief interpretation of what the data suggest about the level of cholesterol.
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