Answer to Question #343602 in Statistics and Probability for justine

Question

One of the psychological tests conducted by the guidance counselors in a public school is the Survey of Study Habits and Attitudes (SSHA) that measures student’s attitudes toward studying. The mean score of Senior High students is with standard deviation of . Mrs. Suacillo suspects that older students have better attitudes toward school. He randomly selects Grade students who are at least years old and gives them SSHA. The test result has a mean score of points. Is there a reason to believe that the claim of the guidance counselors is correct? Assume that the population mean score is normally distributed. Carry out a significance test at level. \

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu\le135$

$H_1:\mu>135$

This corresponds to a right-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 right-tailed test is $z_c = 1.6449.$

The rejection region for this right-tailed test is $R = \{z:z>1.6449\}.$

The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{144.8-135}{35/\sqrt{50}}\approx1.9799$$

Since it is observed that $z=1.9799>1.6449=z_c,$ it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value is $p=P(z>1.9799)=0.023857,$ and since $p=0.023857<0.05=\alpha,$ it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean $\mu$

is greater than 135, at the $\alpha = 0.05$ significance level.