Exercise 1 (40 marks) Naming the ink color of color words can be difficult. For example, if asked to name the colour of the word "blue" is difficult because the answer (red) conflicts with the word "blue." This interference is called "Stroop Interference" after the researcher who first discovered the phenomenon. This case study is a classroom demonstration. Students in an introductory statistics class were each given three tasks. In the "words" task, students read the names of 60 color words written in black ink; in the "color" task, students named the colors of 60 rectangles; in the "interference" task, students named the ink color of 60 conflicting color words. The times to read the stimuli were recorded. There were 31 female and 16 male students. Descriptions of Variables: Variable Description Gender 1 for female, 2 for male Words Time in seconds to read 60 colour words Colours Time in seconds to name 60 colour rectangles Interfer Time in seconds to name colours of conflicting words gender words colours interfer gender words colours Interfere 14 17 38 14 21 49 17 15 58 13 17 40 17 18 35 1 13 17 38 16 20 39 1 12 14 28 1 16 18 33 1 15 18 29 17 20 32 19 24 33 17 20 45 1 14 17 28MNNNNMNNMMMN Note: for this question, you can obtain the relevant mean's and standard deviations from your calculator. a) What is the probability that the average time to read 60 colour rectangles for males will be above 21 seconds? [1" marks} b) What is the probability that the average time to read 60 colour rectangles for females will be between l9 and 24 seconds (exclusive)? ism; c) Construct a 92% confidence interval for the mean time to read 60 colour words for females. {4 ml at) Construct an 80% condence interval for the average time to read 60 colour rectangles for males. Have you appropriately estimated the true population mean? Explain. is marks] e) How large a sample is needed if we wish to be 99% confident that our sample mean to read 60 colour words for females will be within 1.5 seconds of the true mean? Is this sample size reasonable? [5mm] f) Construct a 94% upper confidence bound for "interfer". (4 marks) g) It is considered a success if you can name colours of conflicting words in 33 seconds and less. In the sample for "interfer", set up a 95% confidence interval for the proportion of times in which the population is successful. (3 marks) h) Test at a = 0.01 if there is sufficient evidence to conclude that the average time to read 60 colour rectangles is at least 22 seconds. (6 marks)