SOLUTION: Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies.

Algebra ->  Probability-and-statistics -> SOLUTION: Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies.       Log On


   

Question 1196104:
Do one of the following, as appropriate: (a) Find the critical value zα/2, (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies.
99%; n = 17; σ is unknown; population appears to be normally distributed.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

σ = greek lowercase letter sigma

Because sigma is unknown and because n < 30, this means we cannot use the Z distribution. We must use the T distribution.

df = degrees of freedom
df = n-1
df = 17-1
df = 16

Then use a reference table like this
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
Locate the df = 16 row
Circle everything in this row.

Then circle the column that corresponds to "two tails = 0.01" whch is the third column from the right.

The row and column intersect at the value 2.921
What this means is P(-2.921 < T < 2.921) = 0.99 approximately when df = 16
This gives us the 99% confidence interval, and the 1% rejection region (aka the significance level)

Answer: Approximately 2.921
Use a specialized statistics calculator to get a more accurate value.