Answer: 1.460
Step-by-step explanation:
Given : Researchers report that on average freshman who live on campus gain 15 pounds during their first year in college.
Let [tex]\mu[/tex] represents the population mean .
Then, the set of hypothesis will be:-
[tex]H_0: \mu=15[/tex]
[tex]H_a:\mu\neq15[/tex]
We assume that this is normal distribution.
Sample size : n = 10, which is a small sample (n<30) ,s o we use t-test.
Sample mean : [tex]\overliene{x}=16.2\ lbs[/tex]
Standard deviation : [tex]\sigma=2.6[/tex]
The test statistic for population mean for small sample is given by :-
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]t=\dfrac{16.2-15}{\dfrac{2.6}{\sqrt{10}}}=1.45951276623\approx1.460[/tex]
Hence , the value of test statistic = 1.460
