Answer:
The critical value tα/2 that corresponds to a 98% confidence level with 1000 degrees of freedom is 2.33.
Step-by-step explanation:
From the question we are told that
The critical value is [tex]t_{\frac{\alpha }{2} } = 2.33[/tex]
From the student's t distribution table the probability of [tex]( t > 2.33)[/tex] at a degree of freedom of 1000 is
[tex]\frac{\alpha }{2} = (t > 2.33 ) = 0.01[/tex]
Hence the level of significance is mathematically evaluated as
[tex]\alpha = 2 * 0.01[/tex]
=> [tex]\alpha = 0.02[/tex]
Generally the confidence level is mathematically represented as
[tex]C = 1- \alpha[/tex]
=> [tex]C = 1- 0.02[/tex]
=> [tex]C = 0.98[/tex]
Converting to percentage
=> [tex]C = 0.98 * 100[/tex]
=> [tex]C = 98\%[/tex]
