- A university foreign language department carried out a survey of prospective students to find out which of three languages they were most interested in studying.
A random sample of 150 prospective students gave the following results.
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | Language |
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | French | Spanish | M andarin |
| \multirow{2}{*}{Gender} | M ale | 23 | 22 | 20 |
| \cline { 2 - 5 } | Female | 38 | 32 | 15 |
A test is carried out at the \(1 \%\) level of significance to determine whether or not there is an association between gender and choice of language.
- State the null hypothesis for this test.
- Show that the expected frequency for females choosing Spanish is 30.6
- Calculate the test statistic for this test, stating the expected frequencies you have used.
- State whether or not the null hypothesis is rejected. Justify your answer.
- Explain whether or not the null hypothesis would be rejected if the test was carried out at the \(10 \%\) level of significance.
\section*{Q uestion 1 continued}
\section*{Q uestion 1 continued}
\section*{Q uestion 1 continued}