1. A student gathering information on sociology students gathered a sample with 42 female and 33 male respondents. In this department, we think the distribution of student sex is 60% female and 40% male. Using this data, determine if the distribution of sex in the student's sample of sociology majors is significantly different from the population (a = 0.05). In addition to your ultimate decision, include the chi-square statistic, degrees of freedom, and chi-square critical value. 2. Barnsley et al. (2018) explored the birth month of players in the NHL from the US and Canada. They hypothesized that being born earlier in the year would be associated with higher likelihood of making the pros due to being larger during youth hockey (the cut-off date for youth hockey age brackets is January 1). Using the data below, determine if the distribution of birth months is significantly different from a uniform distribution (a = 0.05). In addition to your ultimate decision, include the chi-square statistic, degrees of freedom, and chi-square critical value. Month Number of Players January February 70 March 79 April 75 May 78 Jung 63 July 46 August 45 September 66 October 38 November 45 December 33 Total 720 3. James Cameron was interested in how survival of the Titanic disaster varied by passenger group. Help him out by determining if survival varied by passenger group (a = 0.05). In addition to your ultimate decision, include the chi-square statistic, degrees of freedom, and chi-square critical valuc. Passenger Group Survived Perished First 202 123 Second 1 18 167 Third 178 508 Total 498 798