Answer to Question #280261 in Statistics and Probability for jack

Question

Scientific and analysis report from Humanization and Social Journal shows the mean of marriage age in Asia region IS at 25.2 years. A random of sampling is taken and as the new result, the of ages of 35 couples had a mean of 28.7 years and a standard deviation of 4.6

years. According to this new sampling, test at the 0.05 level of significance if the mean age of married couples is different from 25.2 years.

Answer 1

We test the following hypotheses;

$H_0:\mu=25.2\space vs \space H_1: \mu\not=25.2$

$n=35, \space \bar{x}=28.7,\space s=4.6,\space \alpha=0.05$

The test statistic is given by,

$t={(\bar{x}-\mu)\over ({s\over\sqrt{n}})}={(28.7-25.2)\over({4.6\over\sqrt{35}})}=4.50$

$t$ is compared with the student's t distribution table value at $\alpha=0.05$ with $n-1=35-1=34$ degrees of freedom given as,

$t_{{0.05\over2},34}=t_{0.025,34}= 2.032245$

The null hypothesis is rejected if, $|t|\gt t_{0.025,34}$

Since $|t|=4.50\gt t_{0.025,34}=2.032245,$ we reject the null hypothesis and conclude that there is sufficient evidence to show that the mean age of married couples is different from 25.2 years at 5% significance level.