Answer:
H0: p1= p2 against the claim Ha: p1≠p2
The data does not supply enough evidence to reject the null hypothesis .
Step-by-step explanation:
The null and alternate hypothesis will be
1) H0: p1= p2 against the claim Ha: p1≠p2
Part b)
Type I Error is when H0 is rejected when it is true.
Type II Error is when H0 is accepted when H0 is false.
In this context Type I Error would be when we would reject the H0 for the above calculations when z does not lie in the critical region.
In this context Type II Error would be when we would accept the H0 when z lies in the critical region.
Part C:
2) The significance level is chosen to be ∝=0.05
3) The critical region for two tailed test is z ≥ ± 1.96
4) The test statistic
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
Here p1= 0.3 and p2= 16/75 =0.213
pc = 30+16/100+75
=0.2629
qc= 1-pc= 1-0.2629= 0.7371
5) Calculations
Z= p1-p2/ sqrt [pcqc( 1/n1+ 1/n2)]
z= 0.3-0.213/√ 0.2629*0.7371( 1/100+ 1/30)
z= 1.294
6) Conclusion
Since the calculated value of z= 1.294 does not lie in the critical region z= ± 1.96 the null hypothesis is accepted and it is concluded that there is no difference between the two proportions.
The data does not supply enough evidence to reject the null hypothesis .
The p - value is 0.1957, which is greater than 0.05 it is concluded that the null hypothesis is not rejected.
