The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 58 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. 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 Hou = 26.6 O H: u = 26.6 OH: H = 26.6 OH: M = 26.6 Part (b) State the alternative hypothesis. OH_: u = 26.6 OH_: u = 26.6 OH: u # 26.6 OH: u = 26.6 Part (c) In words, state what your random variable X represents. O X represents the average age of online students at De Anza College. O X represents the number of online students at De Anza College. O X represents the average age of college students. O X represents the proportion of online students at De Anza College. 9 Part (d) State the distribution to use for the test. (Enter your answer in the form z or t where of is the degrees of freedom.)8 Part (e) What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.) ---Select--- v Part (f) What is the p-value? O p-value 0.100 Explain what the p-value means for this problem. O If He is true, then there is a chance equal to the p-value that the average age of online students is 29.4 years or older. O If He is false, then there is a chance equal to the p-value that the average age of online students is 29.4 years or older. O If He is true, then there is a chance equal to the p-value that the average age of online students is not 29.4 years or older. O If He is false, then there is a chance equal to the p-value that the average age of online students is not 29.4 years or older.El Part {9]- Sketch a picture of this sihiation. Label and scale the horizontal axis and shade the regionjs}: corresponding to the pyalue. Hapvalue} I. limpvalue} Harpvalue} I. limpvalue} fr. it C} 0 El Part{h} :4: p4: Indicate the correct decision ["reject" or "do not reject" the null hypothesis]. the reason for it. and write an appropriate conclusion. [ij Alpha (Enter an exact number as an integer, fraction. or decimal.) {ii} Decision: C} reject the null hypothesis '13 do not reject the null hypothesis [iii] Reason for decision: '13 Since a