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The manager of a restaurant in a large city claims that waiters working in all restaurants in his city earn an average of $150 or more in tips per week. A random sample of 25 waiters selected from restaurants of this city yielded a mean of $139 in tips per week with a standard deviation of $28. Assume that the weekly tips for all waiters in this city have a normal distribution.

a. Using the 1% significance level, can you conclude that the manager's claim is true? Use

both approaches.

b. What is the Type I error in this exercise? Explain. What is the probability of making such

an error?

P Value Approach

Step 1. Write Hypothesis statement.

The null and alternative hypotheses are:

H0?: ??150

H1?: ?

Step 2. State which distribution table will be used.

The the normal distribution table will be used

Step 3. Calculate the P Value

x?=139is the sample mean

?=150is the hypothesised population mean

s =28 is the sample standard deviation

n=25 is the sample size

a. Standard error of the mean( ) 28 = 5.6 25 b. Z = Sample mean- population mean 139-150 -11 = -1.964 standard error of mean 5.6 5.6a. Standard error of the mean( ) 28 = 5.6 25 b. Z = Sample mean- population mean 139-150 -11 = -1.964 standard error of mean 5.6 5.6\f\f