Final answer:
To test the claim about the mean waiting time for bus number 14, we can perform a one-sample t-test using the p-value method. The results suggest that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. This indicates that the filters are effective in reducing the waiting time for bus number 14.
Step-by-step explanation:
To test the claim about the mean waiting time for bus number 14, we can perform a one-sample t-test. The null hypothesis (H0) is that the mean waiting time is equal to 10 minutes, while the alternative hypothesis (Ha) is that the mean waiting time is less than 10 minutes.The test statistic is calculated using the formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is 7.3 minutes, the hypothesized mean is 10 minutes, the sample standard deviation is 1.5 minutes, and the sample size is 18. Substituting these values into the formula, we get:
t = (7.3 - 10) / (1.5 / sqrt(18))
Solving this equation, we find that the test statistic is approximately -5.733. Using the t-distribution table or a calculator, we can find the p-value associated with this test statistic. The p-value represents the probability of obtaining a test statistic as extreme or more extreme than the one observed under the null hypothesis. In this case, the p-value is less than 0.01, which is the significance level. Since the p-value is less than the significance level, we reject the null hypothesis.
The results suggest that there is sufficient evidence to support the claim that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Therefore, we can conclude that the filters are effective in reducing the waiting time for bus number 14.