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The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 11; 5; 13; 3; 11; 8; 8; 10. Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level. Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) State the null hypothesis. O HO: H 10 O Hai H # 10 O Ha: H = 10 Part (c) In words, state what your random variable X represents. O X represents the average number of employees that call out sick on a given day. O X represents the average number of employees that call out sick for 10 days in one year. O X represents the average number of sick days employees take each year. O X represents the number of sick days an employee takes in one year