A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal. The test statistic is a. 1.96. b. 2.00. c. .05. d. 1.65.

Answer: The P-value is between 2.5% and 5% from the t-table.Step-by-step explanation:We are given that a random sample of 16 students selected from the student body of a large university had an average age of 25 years and a standard deviation of 2 years.Let [tex]\mu[/tex] = true average age of all the students at the university.So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 24 years     {means that the average age of all the students at the university is less than or equal to 24}Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 24 years     {means that the average age of all the students at the university is significantly more than 24}The test statistics that will be used here is One-sample t-test statistics because we don't know about the population standard deviation;                                T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~   [tex]t_n_-_1[/tex] where, [tex]\bar X[/tex] = sample average age = 25 years              s = sample standard deviation = 2 years              n = sample of students = 16 So, the test statistics =  [tex]\frac{25-24}{\frac{2}{\sqrt{16} } }[/tex]  ~  [tex]t_1_5[/tex]                                        =  2   The value of t-test statistics is 2. Also, the P-value of test-statistics is given by;             P-value = P( [tex]t_1_5[/tex] > 2) = 0.034 {from the t-table} The P-value is between 2.5% and 5% from the t-table.