Final answer:
Given a p-value of 0.0417 and a significance level of 0.07, there is sufficient evidence to reject the null hypothesis that the difference in binomial probabilities p1 - p2 is zero, indicating a statistically significant difference between the two proportions.
Step-by-step explanation:
The question pertains to independent two-sample hypothesis testing for binomial probabilities. The student is asking to test the null hypothesis H₀:(p₁−p₂)=0 against the alternative hypothesis Hᴇ:(p₁−p₂)≠0 with a significance level of α=0.07, given samples of size 900 from two populations with 254 and 658 successes, respectively.
To proceed with this hypothesis test, one can employ the formula for the test statistic in testing differences between two independent population proportions, which is a Z-test for proportions. This formula looks at the difference between the two sample proportions and divides by the standard error of the difference in proportions. The calculator function 2-PropZTest may be used to obtain the p-value and the test statistic.
If the absolute value of the calculated test statistic is greater than the critical value associated with α=0.07, we will be in the rejection region. The critical value for a two-tailed test at α=0.07 can be found in a standard normal distribution table or with a calculator that provides the corresponding Z-scores.
Based on the information provided (p-value = 0.0417), and since the level of significance (α) given is 0.07, the p-value is smaller than α (0.0417 < 0.07), suggesting the evidence is strong enough to reject the null hypothesis. Hence, we might conclude there is a statistically significant difference between p1 and p2, as the p-value is less than the significance level.