Question

A recent study claimed that the average age of murder victims in a small town was greater than 32.5. A sample of 22 recent victims has a mean of 35.8 years and a standard deviation of 3 years. At a = 0.05, is there enough evidence to support the claim?

Answer 1

Answer)

Null hypothesis Ho : u = 32.5

Alternate hypothesis Ha : u > 32.5

As the population standard deviation is unknown here and we are given with sample s.d as the best estimate

We will use t distribution to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (35.8 - 32.5)/(3/√22) = 5.159

Degrees of freedom is = n-1 = 21

For 21 dof and 5.159 test statistics p-value from t distribution is = 0.000021

Since the obtained P-value is less than the given significance level

We reject the null hypothesis

So, we have enough evidence to conclude that u > 32.5