Question

ACT Scores A survey of 1000 students nationwide showed a mean ACT score of 21.4 . A survey of 500 Washington DC scores showed a mean of 21.3. If the population standard deviation in each case is 3 , can we conclude the national average is greater than the Washington DC average? Use a= 0.01and use u1 for the nationwide mean ACT score.

Part 2 of 5 (b) Find the critical value(s). Round the answer(s) to at least two decimal places. If there is more than one critical value, separate them with commas. Critical value(s):

(c) Compute the test value. Always round

z score values to at least two decimal places.

=z

Answer 1

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 > µ2

Part a)

Critical value Z(α) = Z( 0.01 ) = 2.326

Part b)

Test Statistic :-


Z = 0.61

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Critical value Z(α) = Z( 0.01 ) = 2.326
Z < Z(α) = 0.6086 < 2.326
Result :- Fail to Reject Null Hypothesis