Question

10.3.28-T of complete Letn, -40,X4 - 20. n, -40 and X - 10. Complete parts (a) and (b) below. HW Score: 24.86 a. At the 0.10 level of significance, is there evidence of a significant difference between the two population proportion? Determine the null and alternative hypotheses. Choose the correct answer below O A Ho: 2 252 Hii ng can BM: 512 MC Ho ** MO Calculate the best statisti, ZSTAT, based on the difference P.-P. The statistic, STAT, 231 (Type an integer or a decimal Round to two decimal places as needed.) Calculate the The p-value is (Type an integer or a decimal Round to three decapaces as noded) Enter your answer in the newer box and then click Check Answer parts 2 remaining CA Check Answer MacBook Pro LIBN

Answer 1

p̂1 = 20 / 40 = 0.5
p̂2 = 10 / 40 = 0.25

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 = ( 20 + 10 ) / ( 40 + 40 )
p̂ = 0.375
q̂ = 1 - p̂ = 0.625
Z = ( 0.5 - 0.25) / √( 0.375 * 0.625 * (1/40 + 1/40) )
Z = 2.31
  
Decision based on P value

P value = 2 * P ( Z < 2.31 ) = 0.021

Looking for the value Z = 2.31 in standard normal table to find the P value

Reject null hypothesis if P value < α = 0.1
Since P value = 0.0209 < 0.1, hence we reject the null hypothesis
Conclusion :- We Reject H0