Answer to Question #278951 in Statistics and Probability for nickey

Question

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.

  Using the 1% significance level, can you conclude that the manager’s claim is true?

Answer 1

$H_0:\mu=150$ , waiters working in all restaurants earn an average of $150 or more in tips per week

$H_a:\mu<150$ , waiters working in all restaurants earn an average of less than $150 in tips per week

$t=\frac{\overline{x}-\mu}{\sigma/\sqrt n}=\frac{139-150}{28/5}=-1.964$

$df=n-1=27$

critical value:

$t_{crit}=2.492$

Since $|t|<t_{crit}$ we accept null hypothesis: waiters working in all restaurants earn an average of $150 or more in tips per week.