Question

Mr. X is a high-school history teacher who says that if students are not aware of the Martial Law, then the curriculum should be revised to correct that deficiency. A survey of 506 high-school students showed that 268 of them did not know that the Philippines was under the Martial Law for more than 10 years. Using the sample data and a 0.05 level of significance, test the claim that most (more than 50%) students don’t know what happened during the Martial Law. Based on these results, should Mr. Abad Santos seek revisions to the curriculum?

Answer 1

The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis:

Alternative hypothesis:

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample proportion is too big.

Using sample data, we calculate the standard deviation (σ) and compute the z-score test statistic (z) as follows:

  where is the hypothesized value of population proportion in the null hypothesis, and n is the sample size.

The test statistic is a z-score (z) defined by the following equation:

where is the hypothesized value of population proportion in the null hypothesis, is the sample proportion, and is the standard deviation of the sampling distribution.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 0.003.Thus, the P-Value is obtained as:

Interpret results. Since the P-value (0.4989) is greater than the significance level (0.05), we cannot reject the null hypothesis, and hence conclude that most (more than 50%) students don't know what happened during the Martial Law. Based on these results, Mr. Abad Santos should seek revisions to the curriculum.