I really need help with my statistical analysis... i cant understand it. Here are the questions

Question

A sample group was surveyed to determine which of two brands of soap was preferred. H0 :p = 0.50; H1: p is not equal to 0.50. Thirty-eight of 60 people indicated a preference. At the .05 level of significance, we can conclude that:

The performance of students on a test resulted in a mean score of 25. A new test is instituted and the instructor believes the mean score is now lower. A random sample of 64 students resulted in 40 scores below 25. At a significance level of α = .05:

Answer 1

You can try a proportional one-sample z-test for the first problem since this problem is using proportions.

Here's a few hints to get you started:

Using a formula for a proportional one-sample z-test with your data included, we have:
z = .63 - .50 -->test value (38/60 is approximately .63) minus population value (.50)
divided by
√[(.50)(.50)/60]

Finish the calculation. Remember if the null is not rejected, then there is no difference. If the null is rejected (this is a two-tailed test), then there is a difference and p is not equal to .50.

For the second problem, do the same kind of test. The test proportion will be 40/64 or .625. The sample size is 64. Everything else will be the same as the first problem when plugging the data into the formula. Once you have the test statistic, you can draw your conclusions from there.

Answer 2

I've been trying to work out these problems for about an hour.. I was given multiple choice answers but cannot get my answers even near the ones that were given to me.
Here they are

First problem:

A. z = 0.75, fail to reject H0.

B. z = 1.94, fail to reject H0.

C. z = 1.94, reject H0.

D. z = 2.19, reject H0

second:

A. z = 3.75, we can reject the null hypothesis.

B. z = 1.875, we fail to reject the null hypothesis.

C. z = -1.625, we fail to reject the null hypothesis.

D. z = -1.875, we can reject the null hypothesis.