You said:

Restaurant claims that mean wait time is 3 minutes with sd = 1 minute. Sample of 50 customers found mean = 2.75 minutes. At 0.05 significance, can we conclude that mean wait time is less than 3 minutes?

In general, the null hypothesis is does not include a "greater than" or "less than" statement, rather only an "equals" statement. For example:

Ho: mu = 0

Typically the alternative hypothesis for the mean will include a "greater than", "less than", or "not equal to" statement:

H1: mu < 0

In your case we will set the null hypothesis to what the restaurant claims to be true:

Ho: mu = 3

But since our sample suggested that the mean may be less than that, we would like to test

H1: mu < 3

Next we would like to approximate this problem with the standard normal and define a critical region such that we are 95% confident that the true mean (mu) does not lie within this region.

The critical value for this test is -1.645, that is 95% of the observations from the standard normal distribution will lie above this value. So the critical region is the set of values below -1.645. We know that if our test statistic (Z) is within the critical region then we reject the null hypothesis.

Next is to transform our sample mean to a standard normal random varaible by

Z = Xbar - u/(s/ SQRT(n))

If you made your calculations correctly, -1.77 is within the critical region, and we reject the null hypothesis.

~Matt