Question

Suppose the following hypotheses:

H₀: µ = 2 vs Ha: µ ≠ 2, and σ = 20, sample mean = 12, and use alpha = 0.05

a.     If n = 10 what is p-value?

b.     If n = 15, what is p-value?

c.     If n = 20 what is p-value?

d.     Summarize your findings from above.

Please show your work and thank you SO much in advance! You are helping a struggling stats student SO much!

Answer 1

Part a)

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 12 - 2 ) / ( 20 / √( 10 ))
Z = 1.5811

P value = 2 * P ( Z > 1.5811 ) = 2 * 1 - P ( Z < 1.5811 ) = 0.1139 ( From Z table )

Part b)

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 12 - 2 ) / ( 20 / √( 15 ))
Z = 1.9365

P value = 2 * P ( Z > 1.9365 ) = 2 * 1 - P ( Z < 1.9365 ) = 0.0528 ( From Z table )

Part c)

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 12 - 2 ) / ( 20 / √( 20 ))
Z = 2.2361

P value = 2 * P ( Z > 2.2361 ) = 2 * 1 - P ( Z < 2.2361 ) = 0.0253 ( From Z table )

Part d)

As sample size increases, P value decreases i.e there is more likely that H0 is reject in favor of H1.