Answer: [tex]t= -2.5[/tex]
Step-by-step explanation:
By considering the given statements :
Null hypothesis : [tex]\mu=10[/tex]
Alternative hypothesis : [tex]\mu\neq10[/tex] ( opposite of null hypothesis.)
As per given , we have
Sample size : n= 100
Sample mean : [tex]\overline{x}=9.75[/tex]
Sample standard deviations : [tex]s=1[/tex]
Since population standard deviation is unknown , so we will perform t-test.
Formula for test statistic ( for population mean):
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\=\dfrac{9.75-10}{\dfrac{1}{\sqrt{100}}}\\\\=\dfrac{-0.25}{\dfrac{1}{10}}=-0.25\times10=-2.5[/tex]
Hence, the required test statistic : [tex]t= -2.5[/tex]
