Final answer:
To determine if the mean height of the 31, 18-year-old Filipino teens is significantly different from the population average of 5.2 ft, a one-sample t-test can be conducted. The null hypothesis states that the mean height is equal to 5.2 ft, while the alternative hypothesis states that the mean height is significantly different from 5.2 ft.
Step-by-step explanation:
To determine if the mean height of the 31, 18-year-old Filipino teens is significantly different from the population average of 5.2 ft, we can conduct a hypothesis test. We can use a one-sample t-test since we have the sample mean and standard deviation. The null hypothesis (H0) states that the mean height is equal to 5.2 ft, while the alternative hypothesis (Ha) states that the mean height is significantly different from 5.2 ft.
Next, we calculate the t-test statistic using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). Using the given values, the t-test statistic is t = (5.4 - 5.2) / (7 / sqrt(31)).
Finally, we compare the t-test statistic to the critical value from the t-distribution table at a 99% confidence level with (sample size - 1) degrees of freedom. If the t-test statistic is greater than the critical value or falls within the rejection region, we reject the null hypothesis and conclude that the mean height of the Filipino teens is significantly different from 5.2 ft.