The data set Cold.csv contains the results of a study examining the relationship between taking cold medication and recovery from a cold. It contains two variables:

Medicine taken: This variable takes the value 1 if the person has taken medicine and 0 if they have not taken medicine.

Recover from cold: This variable takes the value 1 if the person recovered from their cold within 3 days and 0 if they took longer than 3 days to recover.

This sample was chosen so that the individual results are statistically independent. These are synthetic data, but you may reference them in your answers as coming from assignment 2 Cold data. The data set has 1000 observations.

Question 3

1. What proportion of participants who recovered within 3 days did take cold medicine compared to those who did not take cold medicine? Report the proportion with the associated 99% confidence interval. Report your results in % and keep 1 decimal place (3 marks).

1. What is your interpretation based on these confidence intervals? (1 mark)

1. How would adjusting the limit to a 90% confidence interval affect the overall interval? (1 mark)

Question 4

1. Can you use a chi square test with these data? Why? (1.5 marks)

1. Test the hypothesis that that there is no association between medicine taken and cold recovery, stating the test statistic to 1 decimal place. As part of your answer, you should:
   • Specify the null and alternative hypotheses. (1 mark)

• Correctly report and interpret the results of the hypothesis test. (3.5 marks)

ID Medicine Recover 1 0 1 2 0 1 3 0 0 4 1 1 5 0 0 6 1 1 7 1 1 TBRCA212222222222222222232333334322144 8 1 1 9 0 1 10 1 0 0 1 0 0 1 1 0 0 15 0 0 16 1 1 17 1 0 18 1 19 0 20 0 0 0 1 0 0 1 0 0 0 25 1 1 26 1 1 27 0 1 28 1 0 29 1 0 30 0 0 0 1 0 0 0 1 0 1 35 0 1 36 0 0 37 1 0 38 1 1 39 0 1 40 0 1 0 0 0 0 1 1 1 0 45 1 1 46 0 1 47 48 49 50 51 oooo C 0 1 0 0 0 0 0 0 1 0 52 0 0 3255526 1 0 54 1 1 1 1 1 1 57 0 1 58 0 1 59 0 1 60 1 0 61 0 1 0 0 1