Question

Please answer all sections as this is one question. Thank you so much!
24. + -18 points BBBasicStat8 10.3.005. My Notes + Ask Your Teacher For one binomial experiment, n = 75 binomial trials produced r = 60 successes. For a second independent binomial experiment, n = 100 binomial trials produced r = 85 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. (a) Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.)
B)

C)

Answer 1

A)

Part a)

p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 60 + 85 ) / ( 75 + 100 )
p̂ = 0.829

Part d)

p̂1 - p̂2 = 0.80 - 0.85 = - 0.05

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √( p̂ * q̂ * (1/n1 + 1/n2) ))
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 60 + 85 ) / ( 75 + 100 )
p̂ = 0.8286
q̂ = 1 - p̂ = 0.1714
Z = ( 0.8 - 0.85) / √( 0.8286 * 0.1714 * (1/75 + 1/100) )
Z = -0.87

Part e)

P value = 2 * P ( Z < -0.87 ) = 0.3851
Looking for the value Z = - 0.87 in Z table to find the P value.

B)

Part a)

α = 0.05

Part b)

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √( p̂ * q̂ * (1/n1 + 1/n2) ))
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 45 + 70 ) / ( 251 + 288 )
p̂ = 0.2134
q̂ = 1 - p̂ = 0.7866
Z = ( 0.1793 - 0.2431) / √( 0.2134 * 0.7866 * (1/251 + 1/288) )
Z = -1.80

Part c)

P value = P ( Z > -1.80 ) = 0.0357

Looking for the value Z = - 1.80 in Z table to find the P value.

C)

Part a)

α = 0.01

Part b)

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √(p̂ * q̂ * (1/n1 + 1/n2) ) )
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 31 + 46 ) / ( 98 + 98 )
p̂ = 0.3929
q̂ = 1 - p̂ = 0.6071
Z = ( 0.3163 - 0.4694) / √( 0.3929 * 0.6071 * (1/98 + 1/98) )
Z = -2.19

Part c)

P value = P ( Z < -2.19 ) = 0.9859
Looking for the value Z = - 2.19  in Z table to find the P value.