Answer:
There is no enough evidence that the probabilities of success for the two binomial experiments differ.
Step-by-step explanation:
The null and alternative hypothesis are:
[tex]H_0: p_2-p_1=0\\\\H_a: p_2-p_1\neq0[/tex]
The significance level is 0.05.
The proportion of the first experiment is p_1=30/75=0.4.
The proportion of the second experiment is p_2=50/100=0.5.
The difference between proportions is
[tex]\Delta p=p_2-p_1=0.5-0.4=0.1[/tex]
The standard deviation of the difference between the proportion is:
[tex]\sigma=\sqrt{\frac{p_2(1-p_2)}{n_2}+\frac{p_1(1-p_1)}{n_1} } \\\\ \sigma=\sqrt{\frac{0.5*0.5}{100}+\frac{0.4*0.6}{75} } \\\\ \sigma=\sqrt{0.0057}=0.075[/tex]
Then, the z-statistic is:
[tex]z=\frac{\Delta p}{\sigma}=\frac{0.1}{0.075} =1.33[/tex]
The p-value for this two-sided test is P(z>1.33)=0.09. This is bigger than the significance level, so the effect is not significant.
There is no enough evidence that the probabilities of success for the two binomial experiments differ.
