1.A study was conducted to explore the association between the heights of young men in secondary school and being bullied at school. "Short" was dened as having a height less than the 5th percentile of the height for young men of the same age. 92 short young men were recruited for the study; 42 of them reported being bullied at school in the last 3 months.

117 young men who were not short were recruited; 30 of them reported being bullied at school in the last 3 months.

Here is a start on laying out these data in a two-way table, in the order epitab wants them laid out. Fill in the missing column.

not bullied bullied total

not short 30 117

short 42 92

1.1What proportion of the young men who are short were bullied at school in the last 3 months?

What proportion of the young men who are not short were bullied at school in the last 3months? Include intermediate steps and details.

1.2What is the relative risk of being bullied at school for the young men who are short,

compared to the young men who are not short?

State the formula you are using in terms of conditional probabilities, along with your rea- soning and intermediate steps/details .

Are the events "a young man is short" and "a young man is bullied at school" independent?

1.3Set up the null and alternative hypotheses for a ² test, using conditional probabilities of the form you calculated in question 1.1.

1.4Check the conditions to use the ² distribution may be used to nd the P value. Explain your reasoning, include all relevant information and show all details.

Set up a matrix in R and carry out the ² test. Paste your matrix and your ² test results here

1.5 State the P value and the conclusion from the ² test. Be concrete and specic

Use the epitab function from the epitools package to nd a 95% condence interval for the relative risk you estimated in question 6.2. Paste your results here:

1.6explain in a sentence interpreting the condence interval for the population relative risk. Explain how your condence interval and the results of the ² test are consistent with eachother