4 Which is closest to the critical tvalues in the exercise s

4) Which is closest to the critical t-values in the exercise?

show work pls

Z~t₅₈

If the critical values are c,d such that c<d then,

P(Z>d)=0.05 that is, P(Z<d)=0.95 and P(Z<c)=0.05

c and d are 0.05 (i.e., 5%) quantile and 0.95 (i.e, 95%) quantile.

Now, refer to a table or run the following code in R

qt(0.95,df=58)

This will give you \"d\". Now, since t-distribution is symmetric we can say c= -d

or run the following code to get \"c\"

qt(0.05,df=58)

Thus, D is the answer.

Method 2

t-distribution converges to a standard normal distribution.

n=58 is quite large.

So, c and d should be close to 5% quantile and 95% quantile of the standard normal distribution which are -1.644854 and 1.644854

The closest option is D.