I am trying to understand the hypothesis test - specifically, which side of the normal curve the rejection region should lie and what my answer means.
Example:
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?
Here is what I did:
Ho: u <= 3; H1: u >3.
Critical value = 1.65 (0.5 - 0.05 = 0.45, z for 0.45)
Z = Xbar - u/(s/ SQRT(n))
= 2.75 - 3/(1/SQRT50)
= -1.77
At a Z of 1.77, my % is 0.46.
Am I correct so far?
To interpret - the likelihood of finding a z value of -1.77 or greater when Ho is true is 0.96 (0 to -1.77, + 0.5 from the right side of the curve). Therefore the Ho is true...
Is this the correct interpretation of the data?
Thank you

Example:
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?
Here is what I did:
Ho: u <= 3; H1: u >3.
Critical value = 1.65 (0.5 - 0.05 = 0.45, z for 0.45)
Z = Xbar - u/(s/ SQRT(n))
= 2.75 - 3/(1/SQRT50)
= -1.77
At a Z of 1.77, my % is 0.46.
Am I correct so far?
To interpret - the likelihood of finding a z value of -1.77 or greater when Ho is true is 0.96 (0 to -1.77, + 0.5 from the right side of the curve). Therefore the Ho is true...
Is this the correct interpretation of the data?
Thank you