Answer: t= -1.60
Explanation:
Let [tex]\mu[/tex] be the population mean weight of pigs.
As per given , we have
[tex]H_0:\mu=230[/tex]
[tex]H_0:\mu\neq230[/tex]
Sample size : n= 16
Sample mean =[tex]\overline{x}=220\ lb[/tex]
Sample standard deviation : [tex]s=25\ lb[/tex]
Since the population standard deviation is not known so the test is a t-test.
Test statistic for population mean : [tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t=\dfrac{220-230}{\dfrac{25}{\sqrt{16}}}[/tex] (Substitute all the values.)
[tex]t=\dfrac{-10}{\dfrac{25}{4}}[/tex]
[tex]t=\dfrac{-40}{25}=-1.60[/tex]
Hence, the value of the test statistic needed to test the null hypothesis : t= -1.60
