Answer:
The P-value ranges between 2.5% and 5% according to the t-table.
Step-by-step explanation:
A random sample of 16 students from a large university showed an average age of 25 years with a standard deviation of 2 years.
Let = true average age of all students at the university.
So, the Null Hypothesis, :
24 years {indicating the average age is less than or equal to 24 years}
Alternate Hypothesis, :
> 24 years {indicating the average age is significantly greater than 24 years}
Here we employ the One-sample t-test statistics as the population's standard deviation is unknown;
T.S. = ~
where, = sample average age = 25 years
s = sample standard deviation = 2 years
n = sample size = 16
This gives us the test statistics = ~
= 2
The value of the t-test statistics is 2.
Moreover, the P-value of the test-statistics can be found as follows;
P-value = P( > 2) = 0.034 {as per the t-table}
Thus, the P-value lies between 2.5% and 5% based on the t-table.