As part of a larger study, Bratanova et al. (2015)1 investigated whether a person's taste for biscuits could be influenced by the ethicality of the manufacturing company. A fictional biscuit company was used for the study. 112 undergraduate students from a Belgian university volunteered to participate in the study.

The students were randomly assigned to one of two groups: 53 to a group that were given a description that portrayed the company as environmentally friendly and the remaining 59 to another group that were given a description that portrayed the company as environmentally harmful.

Students in both groups were then given the same type of biscuit to taste and told that it was made by the company in the description. After tasting the biscuit, both groups of students were asked to rate on a 7-point scale how likely it was that they would buy biscuits from this company in the future (Future buy).

For the purpose of analysing this data we will treat Future buy as a numeric variable where 1 = not at all likely, and 7 = very likely.

a. Carry out a two-tailed randomisation test to investigate whether there is a difference between the underlying mean future buy rating for companies portrayed as environmentally friendly and the underlying mean future buy rating for companies portrayed as environmentally harmful. An approximate 95% confidence interval for the difference between the underlying means described above (Friendly - Harmful) is (0.05, 1.31). Interpret this confidence interval as part of the test.

b. Make a Step-By-Step Guide to perform the Hypothesis Test by hand

c. Does the confidence interval given in part a contain the true value of the parameter? Briefly explain.

\fSummary of Future_buy by Group: Estimates Min 25% Median 75% Max Mean SD Sample Size Friendly 1 3 5 5 7 4.377 1.757 53 Harmful 2 4 5 7 3. 695 1.653 59