Answer to Question #206267 in Statistics and Probability for kel

Question

A study was conducted to determine the marrying age of teachers. It was found out

that the mean marrying ager of teachers is 30 years old. Fifteen teachers were surveyed

randomly and found that their mean marrying age was 33 years old with a standard

deviation of 5 years. Use 10% level of significance to test the hypothesis and assume that

the population is normally distributed.

Answer 1

$H_0: \mu=30 \\ H_1: \mu ≠ 30 \\ t = \frac{\bar{x}- \mu}{s/ \sqrt{n}} \\ \bar{x}=33 \\ s=5 \\ n=15 \\ α=0.1 \\ df=n-1=14 \\ t = \frac{33-30}{5/ \sqrt{15}}=2.323 \\ t_{crit}=2.144 \\ t> t_{crit}$

Reject H₀.

Their average age is not 30 years.