Answer to Question #115877 in Statistics and Probability for Shane Jessica Ballera

Question

Hypothesis Testing

According to the Journal of Counseling Psychology, forbearance is a coping strategy of collectivist society with 150 Chinese respondents scoring an average of 35 with a standard deviation of 7 in a ten item forbearance scale. You want to test if Europeans use the same coping strategy andyou found that they scored an average of 25 in the same forbearance scale in a thesis. Discuss your finding findings at α 0.05 in traditional and p-value method.

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=35$

$H_1:\mu\not=35$

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

Based on the information provided, the significance level is $\alpha=0.05,$ and the critical value for a two-tailed test is $z_c=1.96.$

The rejection region for this two-tailed test is $R=\{z:|z|>1.96\}.$

The z-statistic is computed as follows:

$$z={\bar{X}-\mu\over \sigma/\sqrt{n}}={25-35\over 7/\sqrt{150}}\approx-17.496$$

Since it is observed that $|z|=17.496>z_c=1.96,$ it is then concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population mean $\mu$  is different than 35, at the 0.05 significance level.

Using the P-value approach: The p-value is $p=0,$ and since $p=0<0.5,$ it is concluded that the null hypothesis is rejected. Therefore, there is enough evidence to claim that the population mean $\mu$ is different than 35, at the 0.05 significance level.