Answer to Question #281188 in Statistics and Probability for Mao

Question

The average hospitality girls working in a certain area is 19 years old. A civic oriented group made a recent survey on the age of the hospitality girls working in the same locality. A random sample of 20 respondents showed an average of 15.4 years old with a standard deviation of 2.14 years old. Using a 0.05 level of significance, has the hospitality girls gone lower?

Answer 1

$H_0:\mu=19$ , average hospitality girls working in a certain area is 19 years old

$H_a:\mu<19$ , average hospitality girls working in a certain area is less than 19 years old

$t=\frac{\overline{x}-\mu}{\sigma/\sqrt n}=\frac{15.4-19}{2.14/\sqrt{20}}=-7.523$

$df=n-1=19$

critical value:

$t_{crit}=1.729$

Since $t<-1.729$ we reject null hypothesis. Average hospitality girls working in a certain area is less than 19 years old.