Final answer:
The hypothesis test aims to determine whether the proportion of high school girls who have done strenuous exercise is less than 0.50. The test statistic is calculated and compared to critical values, while the p-value determines if there's sufficient evidence to reject the null hypothesis at the 0.05 significance level.
Step-by-step explanation:
To test the hypothesis using a traditional and p-value approach, we first set up the null hypothesis (H0) that the population proportion (p) of high school girls who do strenuous exercise is 0.50, and the alternative hypothesis (Ha) that this proportion is less than 0.50. We are using a significance level (alpha) of 0.05. The test statistic for a single population proportion is calculated using the formula (p' - p) / sqrt((p(1 - p) / n)), where p' is the sample proportion, p is the hypothesized population proportion, and n is the sample size. In this case, with 400 out of 850 girls having done strenuous exercise, p' is 400/850.
The test statistic is then compared to the critical value from the standard normal distribution table to determine whether to reject the null hypothesis. The p-value is the probability of observing a test statistic as extreme as the sample result, under the null hypothesis. If the p-value is less than or equal to alpha, we reject the null hypothesis.
Conclusion
If the calculated p-value is less than 0.05, there is sufficient evidence to reject the null hypothesis and conclude that the proportion of high school girls who have done strenuous exercise is less than 0.50.