Answer: 1.205
Step-by-step explanation:
Given : Significance level : [tex]\alpha=0.025[/tex]
[tex]H_0:\mu=50.6\\\\H_1:\mu>50.6[/tex]
We assume that population is normally distributed.
The sample size : [tex]n=10[/tex], which is less than 30 , so we apply t-test.
Mean : [tex]\overline{x}=54.6[/tex]
Standard deviation : [tex]\sigma=10.5[/tex]
The test statistic for population mean is given by :-
[tex]t=\dfrac{\overline{x}-\mu_0}{\dfrac{\sigma}{\sqrt{n}}}\\\\=\dfrac{54.6-50.6}{\dfrac{10.5}{\sqrt{10}}}=1.20467720387\approx1.205[/tex]
Hence, the critical value = 1.205
