Question

Consider the following hypotheses:

H0: μ ≤ 350

HA: μ > 350

Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table)

a. x¯x¯ = 363; s = 29; n = 18

( ) p-value < 0.01
( ) p-value 0.10
( ) 0.01 p-value < 0.025
( ) 0.05 p-value < 0.10
( ) 0.025 p-value < 0.05

b. x¯ = 363; s = 29; n = 36

( ) p-value < 0.01
( ) 0.05 p-value < 0.10
( ) 0.01 p-value < 0.025
( ) 0.025 p-value < 0.05
( ) p-value 0.10

c. x¯ = 363; s = 16; n = 12

( ) 0.025 p-value < 0.05
( ) 0.01 p-value < 0.025
( ) p-value < 0.01
( ) 0.05 p-value < 0.10
( ) p-value 0.10

d. x¯ = 358; s = 16; n = 12

( ) 0.01 p-value < 0.025
( ) p-value 0.10
( ) 0.025 p-value < 0.05
( ) p-value < 0.01
( ) 0.05 p-value < 0.10

Answer 1

Part a)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 363 - 350 ) / ( 29 / √(18) )
t = 1.9019

P - value = P ( t > 1.9019 ) = 0.0371 ( From t table )

( ) 0.025 p-value < 0.05

Part b)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 363 - 350 ) / ( 29 / √(36) )
t = 2.6897

P - value = P ( t > 2.6897 ) = 0.0054

( ) p-value < 0.01

Part c)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 363 - 350 ) / ( 16 / √(12) )
t = 2.8146

P - value = P ( t > 2.8146 ) = 0.0084 ( From t table )

( ) p-value < 0.01

Part d)

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 358 - 350 ) / ( 16 / √(12) )
t = 1.7321

P - value = P ( t > 1.7321 ) = 0.0556

( ) 0.05 p-value < 0.10