A random sample of 80 GCSE students was selected to take part in an investigation into whether attitudes to mathematics differ between girls and boys. The students were asked if they agreed with the statement 'Mathematics is one of my favourite subjects'. They were given three options 'Agree', 'Disagree', 'Neither agree nor disagree'. The results, classified according to sex, are summarised in the table below.
Agree
Disagree
Neither
Male
17
13
8
Female
12
11
19
The contributions to the test statistic for the usual \(\chi ^ { 2 }\) test are shown in the table below.
Agree
Disagree
Neither
Male
0.7550
0.2246
1.8153
Female
0.6831
0.2032
1.6424
Calculate the expected frequency for females who agree. Verify the corresponding contribution, 0.6831 , to the test statistic.
Carry out the test at the \(5 \%\) level of significance.
The level of radioactivity in limpets (a type of shellfish) in the sea near to a nuclear power station is regularly monitored. Over a period of years it has been found that the level (measured in suitable units) is Normally distributed with mean 5.64. Following an incident at the power station, a researcher suspects that the mean level of radioactivity in limpets may have increased. The researcher selects a random sample of 60 limpets. Their levels of radioactivity, \(x\) (measured in the same units), are summarised as follows.
$$\sum x = 373 \quad \sum x ^ { 2 } = 2498$$
Carry out a test at the \(5 \%\) significance level to investigate the researcher's belief.