Question

# A random sample of 16 students selected from the student body of a large university had...

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 less than equal to or greater than 24. Assume the distribution of the population of ages is normal. Using α = .05, it can be concluded that the population mean age is

 not different than 24. different from 24. greater than 24 less than 24

Given that,

H0: = 24

Ha: > 24

Test statistics

t = - / S / sqrt(n)

= 25 - 24 / 2 / sqrt(16)

= 2

Degrees of freedom = n-1=16-1=15

= level of significance=0.05

this is one tailed (right) test

Now, we can find the P-value

P-value = 0.0320 ( using EXCEL =TDIST(x,D.F,tail))

P-value < 0.05 ()

That is we reject Ho (Null Hypothesis)

We conclude that we have sufficient evidence to support the claim that mean age is

greater then 24 (significantly more than 24)

Option C is correct.

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