The probability of a student playing football is known to be 0.53; and the probability of...

The probability of a student playing football is known to be 0.53; and the probability of a student playing rugby is known to be 0.5. If the probability of playing both is known to be 0.38, calculate:

(a) the probability of playing rugby

(b) the probability of playing at least one of football and rugby

(c) the probability of a student playing rugby, given that they play football

(d) Are playing rugby and football independent? Justify

(e) (harder) a group of 29 randomly selected students attend a special seminar on the health benefits of playing sport. Of these 29, only 5 play neither after the seminar. State a sensible null hypothesis, test it, and interpret.

Notes:
• Show detailed working, including appropriate mathematical notation for each question. For most questions this will involve showing your working from R Studio, (e.g. cut-and-paste commands and output from an R session).

• Any question involving regression will score 0 marks unless a scattergraph is produced.

•No Additional Info provided

Expert Solution

The screenshot for the test statistic calculations in R has been attached.

orchestra answered 1 year ago

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