Question

Given a variable that has a t distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region? (Round your answers to one decimal place.)

(a) 10 df, between -1.81 and 1.81
%

(b) 10 df, between -2.23 and 2.23
%

(c) 24 df, between -2.06 and 2.06
%

(d) 24 df, between -3.47 and 3.47
%

(e) 24 df, outside the interval from -2.80 to 2.80
%

(f) 24 df, to the right of 2.80
%

(g) 10 df, to the left of -1.81
%

Answer 1

we see that for df = 10 and t = 1.81 the t values in percentage are
t0.05
so negative would be

0.95

hence the area between the 2 values would be

0.95-0.05 = 0.90

b
we see that for df = 10 the t values in percentage are
t0.025
so negative would be

0.975

hence the area between the 2 values would be

0.975-0.025 = 0.95

c
again we check the df - 24 and t 0.025 which is 2.06
so
so negative would be

0.975

hence the area between the 2 values would be

0.975-0.025 = 0.95

d
similarly for df = 24 and value = 3.74 we see that the t percetnage is 0.0005
so opposite end of the curve would be
0.9995
so the area is
0.9995-0.0005
= 0.999

Please note that we can answer only 4 subparts of a question at a time