For one binomial experiment, n1 = 75 binomial trials produced r1 = 30 successes. For a second independent binomial experiment, n2 = 100 binomial trials produced r2 = 50 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ.

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:

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

The standard deviation of the difference between the proportion is:

Then, the z-statistic is:

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.

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step-by-step explanation: