Problem 2E

Find the value of tn-1,α needed to construct an upper or lower confidence bound in each of the situations in Exercise 1.

Answer:

Step 1 of 5:

Here we have to find the value of needed to construct an upper or lower confidence bound in each of the given level with the given sample size in exercise 1.

Step 2 of 5:

a). Given that the confidence level is 90% and the sample size is n = 12.

Then,

% = 90% =

(1 - 0.9) = 0.1

Therefore,

The level of significance

And the degrees of freedom, DF = n - 1

= 12-1

= 11

Therefore, the critical value of ‘t’ is

( This value from statistical table, 11th row and 0.1 column)

Then,

Lower bound < t < upper bound

-1.363 < t < 1.363

Step 3 of 5:

b). Given that the confidence level is 95% and the sample size is n = 7.

Then,

% = 95% =

(1 - 0.95) = 0.05

Therefore,

The level of significance

And the degrees of freedom, DF = n - 1

= 7-1

= 6

Therefore, the critical value of ‘t’ is

( This value from statistical table, 6th row and 0.05 column)

Then,

Lower bound < t < upper bound

-1.943 < t < 1.943