As part of an investigation into smoking, a random sample of 120 students was selected. The students were asked whether they were smokers, and also whether either of their parents were smokers. The results are summarised in the table below. Test, at the \(5 \%\) significance level, whether there is any association between the smoking habits of the students and their parents.
At least one
parent smokes
Neither parent
smokes
Student smokes
21
27
Student does not smoke
17
55
The manufacturer of a particular brand of cigarette claims that the nicotine content of these cigarettes is Normally distributed with mean 0.87 mg . A researcher suspects that the mean nicotine content of this brand is higher than the value claimed by the manufacturer. The nicotine content, \(x \mathrm { mg }\), is measured for a random sample of 100 cigarettes. The data are summarised as follows.
$$\sum x = 88.20 \quad \sum x ^ { 2 } = 78.68$$
Carry out a test at the \(1 \%\) significance level to investigate the researcher's belief.
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