Answer to Question #280214 in Statistics and Probability for Deandra

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.

Answer 1

Null hypothesis $H_0:\mu=150.$

Alternative hypothesis $H_a:\mu<150.$

Test statistic: $t=\frac{\bar x-\mu}{\frac{s}{\sqrt{n}}}=\frac{139-150}{\frac{28}{\sqrt{25}}}=-1.96.$

Degrees of freedom: $df=n-1=25-1=24.$

P-value: $p=P(T<-1.96)=0.0309.$

Since the p-value is less than 0.05, reject the null hypothesis.

There is a sufficient evidence that waiters working in all restaurants in his city earn an average less than $150.