Question

A) If you have a t-distribution with 27 degrees of freedom, what value cuts off the upper 2.5% (to 6 decimal places)?

B ) If you have an F-distribution with 2 numerator degrees of freedom and 24 denominator degrees of freedom, what is the probability of an F-ratio less than or equal to 3 (to 7 decimal places)?

C) If we have an F-distribution with 12 numerator degrees of freedom and 30 denominator degrees of freedom, what value cuts off the upper 12.23% (to 6 decimal places)?

D) Which function allows you to draw random numbers from the t-distribution?

E)Which function allows you to find the the probability of a value being less than or equal to some q in the chi-square distribution?

F) Use your knowledge of the normal distribution functions to answer the following question.

Which of the following responses gives the highest probability?

Answer 1

A) df = 27

We need to find,

p ( t > t_calculated ) = 0.025

1 - p ( t < t_calculated ) = 0.025

p ( t < t_calculated ) = 0.975

t_calculated = 2.051831

B) df_N = 2, df_D = 24

p ( F 3 ) = 0.931281 ---------- (using Fdist function )

c) df_N = 12, df_D = 30

p ( F > F_calculated ) = 0.025

1 - p ( F < F_calculated ) = 0.1223

p ( F < F_calculated ) = 0.8777

_Fcalculated = 1.679099

D) Function " = TINV(RAND(),df)*RANDBETWEEN(botttom, top ) " allows you to draw random numbers.