A website is trying to increase registration for first-time visitors, exposing a random sample of 1% of visitors to the design, over the course of three months in early 2020. Of 752 randomly sampled visitors over a month who saw the new design, 64 registered for the site.

Now, imagine that the analytics team has data that shows that the old website had a registration rate of 7.5%. You'll now do a hypothesis test to see if there is strong statistical evidence that the new website significantly better or worse than the original design.

a. Find the null hypothesis.

b. Find the the alternative hypothesis.

c. Compute the standard error for use in the hypothesis test.

d. Calculate the z-score for the p-hat, for the null distribution.

e. What is the p-value for this two-sided hypothesis test?

f. Interpret the p-value at the alpha = 0.05 significance level. Make sure you put it in context of the study, and clearly state if you reject or fail to reject the null hypothesis (and why).