Anagrams are words or phrases where all of the letters are rearranged to form a new word. For example, the name Eric is an anagram of rice. One may also consider:

• the anagram of twelve plus two is eleven plus one
• The eyes is an anagram of They see
• Dormitory is an anagram of dirty room.

The importance of anagrams in psychology is apparent when considering the mental dexterity required for solving an anagram puzzle.

A pharmaceutical company has produced a new drug to treat heart disease which is believed may reduce the mental dexterity of those individuals who have been administered it. A sample of 18 individuals was randomly chosen and assigned to one of two treatment groups: a placebo; and, 50mg of the drug. Once the drug condition was administered each of the individuals underwent an anagram test of equal complexity. Their performance on the test was scored out of 20; a high score indicates that the patient had high mental dexterity, while a low score reflected that the patient had low dexterity in the anagram test.

a. The company is interested in testing for a reduction in the mental dexterity of an individual if they take the new drug. For making such a comparison, define appropriate null and alternative hypotheses. Use Rstudio

b. Using an appropriate statistical test, determine the test statistic, the associated degrees of freedom and the p-value. Justify the test you have used. Use Rstudio

c. Provide a decision about the null hypothesis at the 1% significance level as well as a practical conclusion that would answer the researchers question Is there a reduction in the mean mental dexterity score for individuals who were administered the drug when compared with those given the placebo? Use Rstudio

d. State any assumptions that have been made when performing this test and provide comment on their suitability. Use Rstudio

e. Provide a 99% confidence interval that may be used to test the same hypothesis you provided in part e. Use this interval to test the hypothesis. Use Rstudio

f.Calculate the power to detect a difference in dexterity scores of 4, assuming the standard deviation is 2.4 and the significance level is 1% and the sample size is 9. Use Rstudio

D A B score C treatment 15 Placebo 11 Placebo 18 Placebo 9 Placebo 14 Placebo 13 Placebo 17 Placebo 13 Placebo 15 Placebo 9 Drug 12 Drug 14 Drug 6 Drug 8 Drug 8 Drug 10 Drug 9 Drug 11 Drug D A B score C treatment 15 Placebo 11 Placebo 18 Placebo 9 Placebo 14 Placebo 13 Placebo 17 Placebo 13 Placebo 15 Placebo 9 Drug 12 Drug 14 Drug 6 Drug 8 Drug 8 Drug 10 Drug 9 Drug 11 Drug