Question

Find the value x for which: (Round your answers to 3 decimal places. You may find it useful to reference the appropriate table: chi-square table or F table) x a

. P( χ217 ≥ x) = 0.900 b. P( χ217 ≥ x) = 0.950 c. P( χ217  <   x) = 0.900 d. P( χ217 < x) = 0.950

Answer 1

Solution:

We have to find value of x for given probabilities using appropriate tables.

Since probabilities are given for Chi-square distribution, we use Chi-square critical value table.

Part i)

Chi-square critical value table gives right tail probabilities for given df values.

Thus look in Chi-square critical value table for df = 17 and right tail area = 0.900 and find corresponding Chi-square critical value.

Thus x = 10.085

that is:

Part ii)

Look in Chi-square critical value table for df = 17 and right tail area = 0.950 and find corresponding Chi-square critical value.

Thus x = 8.672

thus

Part iii)

Since Chi-square critical value table gives right tail probabilities for given df values and above probability is left of x , we need to find corresponding right tail area.

If then

Thus look in Chi-square critical value table for df = 17 and right tail area = 0.10 and find corresponding Chi-square critical value.

Thus x = 24.769

thus

that is:

Part iv)  

Since Chi-square critical value table gives right tail probabilities for given df values and above probability is left of x , we need to find corresponding right tail area.

If then

Thus look in Chi-square critical value table for df = 17 and right tail area = 0.050 and find corresponding Chi-square critical value.

Thus x = 27.587

that is:

that is: