You have an SRS of size 8 and calculate the one-sample t statistic. What is the critical value t∗ such that (a) t has probability 0.02 to the right of t∗? (b) t has probability 0.85 to the left of t∗?

a) "=T.INV(1-0.02,7)"

And we got

b) "=T.INV(0.85,7)"

And we got

Step-by-step explanation:

For this case we have a sample size of n=8, so we can find the degrees of freedom like this:

Part a

For this case we need a value who accumulates 0.02 of the area in the right of the t distribution with 7 degrees of freedom so we can use the following excel code:

"=T.INV(1-0.02,7)"

And we got

Part b

For this case we need a value who accumulates 0.85 of the area in the left of the t distribution with 7 degrees of freedom so we can use the following excel code:

"=T.INV(0.85,7)"

And we got

what graph

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for