5 A researcher is investigating whether there is any relationship between the overall performance of a student at GCSE and their grade in A Level Mathematics. Their A Level Mathematics grade is classified as A* or A, B, C or lower, and their overall performance at GCSE is classified as Low, Middle, High.
Data are collected for a sample of 80 students in a particular area. The researcher carries out a chi-squared test. The screenshot below shows part of a spreadsheet used to analyse the data. Some values in the spreadsheet have been deliberately omitted.
| 1 | A | B | C | D | E |
\multirow{2}{*}{| } | Observed frequency | | | | A* or A | B | C or lower | Totals | | 3 | Low | 6 | 13 | 9 | 28 | | 4 | Middle | 10 | 6 | 8 | 24 | | 5 | High | 15 | 10 | 3 | 28 | | 6 | Totals | 31 | 29 | 20 | 80 | | 7 | | | 8 | \multirow{2}{*}{} | | | | 9 | | A* or A | B | C or lower | | | 10 | Low | 10.85 | | | | | 11 | Middle | 9.30 | | | | | 12 | High | 10.85 | | | | 13 | \multirow[b]{2}{*}{Contribution to the test statistic} | | | 14 | | | | | | | 15 | | A* or A | B | C or lower | | | 16 | Low | 2.1680 | 0.8002 | 0.5714 | | | 17 | Middle | 0.0527 | 0.8379 | 0.6667 | | | 18 | High | 1.5873 | | | | 19 | | | | | |
- State what needs to be known about the sample for the test to be valid.
For the remainder of this question, you should assume that the test is valid.
- Determine the missing values in each of the following cells.
- C11
- C18
- In this question you must show detailed reasoning.
Carry out a hypothesis test at the \(10 \%\) significance level to investigate whether there is any association between level of performance at GCSE and A Level Mathematics grade. - Discuss briefly what the data suggest about A Level Mathematics grade for different levels of performance at GCSE.
- State one disadvantage of using a 10\% significance level rather than a 5\% significance level in a hypothesis test.
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