Question 4. [ 21 marks ] [ Second half of Chapter 8] (f) Assume the Tukey's pairwise comparisons are valid and appropriate. (Note: They may not be.) A Sudoku puzzle is completed using given numbers, letters or symbols to fill in a grid. Two statistics (i) Investigate whether, on average, there is a difference between the time taken to correctly lecturers decided to investigate whether the characters used in the puzzle affected the time taken to complete the puzzle when the Sudoku type is a Number character and when the Sudoku type complete the puzzle. The 227 participants in the study were all students in an introductory statistics is a Greek character. Interpret the P-value and confidence interval. class at an Irish university. Note: A conclusion is not required here. [ 2 marks ] Usually Sudoku puzzles are completed on a 9 by 9 grid. To reduce the time needed to complete the (ii) Between which pair (or pairs) of Sudoku types were there significant differences (at the 5% puzzles, a 6 by 6 Sudoku grid was used instead. All puzzles had the same layout but four different types level) in the mean time taken to correctly complete the puzzle? [ 1 mark ] of characters were used (Greek, Letter, Number, Symbol ) as shown in the table below: (iii) Are we able to determine which Sudoku type has the fastest (i.e., lowest) underlying mean time taken to correctly complete the puzzle? If so, name the character type. [ 1 mark ] Sudoku type Characters Greek (g) In three to five sentences, provide an overall conclusion for this study. [ 4 marks ] Letter a Number 1 2 5 Symbol Computer output from SPSS for use in Question 4 (e) to (@) Students were randomly allocated to one of the four Sudoku types. Puzzles were completed under test conditions. A clock was displayed which students used to record the time (in seconds) taken to correctly ANOVA complete their puzzle. Time (seconds) Sum of Squares df Mean Square F Sig Note: Use the computer output from SPSS given to the right to answer (e) to (g)- Between Groups 389465.706 3 129821.902 16.032 000 (a) For this study describe the: [ 1 mark ] Within Groups 1805799.712 223 8097.757 Total 2195265.419 226 (i) units, (ii) treatment or factor of interest, (iii) response. Multiple Comparisons Dependent Variable: Time (seconds) (b) (i) Use iNZight to draw the appropriate plots for this data set. [ 1 mark ] Tukey HSD (ii) Comment on any features in the plots in terms of the original story. [3 marks ] Mear 95% Confidence Interval (0) Sudoku type (J) Sudoku type Difference (I-J) Sid. Error Sig- Lower Bound|Upper Bound (c) Use iNZight to get summary statistics for this data and calculate the ratio of the largest sample standard deviation to the smallest sample standard deviation. (Note: The ratio of A to B is A divided Greek Letter 66.182 17.186 001 21.70 110.67 by B.) [ 1 mark ] Number 10.695 16.985 .000 66.73 154.66 Note: The data file SudokuData . cav is available on Canvas under Assignments > Assignment 3. Symbol 29.668 17.330 320 -15.19 74.53 Letter Greek 66.182 17.186 .001 110.67 21.70 (d) Comment on the validity of the F-test by briefly discussing each assumption in terms of the original 44.512" 16.504 .038 1.79 87.23 story. [ 4 marks ] Number Symbol 36.515 16.859 80.15 7.12 (e) Assume that an F-test is an appropriate test to use here. (Note: It may not be.) Number Greek -110.695 6.985 .000 154.66 66.73 (i) State the null hypothesis for the test, both in words and using symbols. [ 1 mark ] Letter 44.512 16.504 038 -87.23 -1.79 (ii) State the alternative hypothesis for the test in words. [ 1 mark ] Symbol 81.027 16.654 000 -124.14 37.92 Symbol Greek 29.668 17.330 320 74.53 15.19 (iii) What does the result of the F-test tell you about the underlying mean time taken to correctly complete the puzzle for the four Sudoku types? [ 1 mark ] Letter 36.515 16.859 136 -7.12 80.15 Number 81.027 16.654 .000 37.92 124.14 . The mean difference is significant at the 0.05 level