Questions 1 and 4 refer to the following information. A study was conducted to investigate gender stereotypes in children aged 5 to 7 years (Bian et al., 2017)'. In one part of the study2 children were shown pictures of eight pairs of adults (One female and one male per pair) and were asked to say which adult in each pair was \"really really smart\". Each pair was matched for attractiveness and professional dress (potential cues for intelligence). The researchers recorded the number of times (out of 8 trials) the child chose their own sex as being smart. Similarly the children were also asked to say which adult in each pair was \"really really nice\". Part of the spreadsheet for the 144 children in this part of the study is shown below: A B C D 1 Sex Age Smart Nice 2 Boy 6 year-old 7 3 3 Boy 5 year-old 7 6 4 Boy 7year-old 4 5 5 Girl 5 year-old 8 6 6 Boy 5 year~old 5 5 The variables recorded are dened as: Sex The sex of the child (Bo y, Girl) Age The age group ofthe child (5 yearold, 6 yearold, 7 yearold) Smart The number of times (out of 8 trials) the child chose their own sex as being smart Nice The number of times (out of 8 trials) the child chose their own sex as being nice Question 1. [ 9 marks ] [Chapter 7] Summary statistics of Nice by Sex are displayed below: (a) (II) Summary of Nice by Sex: Estimates Min 25% Median 75% Max Mean SD Sample Size Boy 8 3 4.5 6 8 4.264 2.149 72 Girl 1 5 6.6 7 8 5.958 1.448 72 Carry out a t-test to investigate whether there is a difference between the underlying mean number of times (out of 8 trials) girls chose their own sex as being nice and the underlying mean number of times (out of 8 trials) boys chose their own sex as being nice. [8 marks] Notes: (i) You must clearly show that you have followed the \"Step-by-Step Guide to Performing a Hypothesis Test by Hand\" given in the Lecture Workbook, Chapter 7, blue page 14. (ii) At Steps 5 and 8, it is necessary to use the t-procedures tool on Canvas (Assignments > Assignment 3) to determine the standard error and the tmultiplier. (iii) At Step 6, it is necessary to use the z-procedures tool on Canvas to determine the Pvalue. (iv) Refer to the instructions on page 1 of this assignment: \"Hypothesis tests in this assignment\". Does the condence interval given in part (a) contain the true value of the parameter? Briey explain. [ 1 mark]