Question

Consider the following hypotheses:
H₀: μ = 380
H_A: μ ≠ 380
The population is normally distributed with a population standard deviation of 63.

a-1. Calculate the value of the test statistic with x−x− = 393 and n = 95. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

a-2. What is the conclusion at the 10% significance level?

a-3. Interpret the results at αα = 0.10.

b-1. Calculate the value of the test statistic with x−x− = 359 and n = 95. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b-2. What is the conclusion at the 5% significance level?

b-3. Interpret the results at αα = 0.05.

Answer 1

Part a-1)

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 393 - 380 ) / ( 63 / √( 95 ))
Z = 2.01

Part a-2)
Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.1 /2 ) = 1.645
| Z | > Z( α/2 ) = 2.0112 > 1.645
Result :- Reject null hypothesis

Part a-3)

There is sufficient evidence to support the claim that   μ ≠ 380 at 10% level of significance.

part b-1)

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 359 - 380 ) / ( 63 / √( 95 ))
Z = -3.25

Part b-2)

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.05 /2 ) = 1.96
| Z | > Z( α/2 ) = 3.2489 > 1.96
Result :- Reject null hypothesis

Part b-3)

There is sufficient evidence to support the claim that   μ ≠ 380 at 5% level of significance.