Test of Hypothesi: Mean Waiting Time

The Restaurants McBurger says that the waiting time for customers is 3 minutes with a standard deviation of population 1 minute. The quality control department found in a sample of 50 clients that the average waiting time was 2.75 minutes. With a significance level of 0.05. Can conclude that the waiting time is less than 3 minutes?

Please provide details for I try to understand the procedure.

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1) Hypothesis
Null Hypothesis: Ho: M = 3 (:Mean is 3 minutes)
Alternative Hypothesis: H1: M < 3 :( Mean is less than 3 minutes )
Significance level=alpha (a) = 0.05 or 5%
No of tails= 1 ( Left tail )
This is a 1 tailed ( Left tail ) test because we are testing that M < 3

2) Decision rule
sample size=n= 50
Since sample size is more than 30 and population standard deviation is known, use normal distribution
Thus we use z distribution
Z at the 0.05 level of significance 1 tailed test = 1.6449
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