Respuesta :
Answer:
Step-by-step explanation:
To calculate a 95% confidence interval for the mean speed of all cars on Triphammer Road, we can use the following steps:
1. Calculate the sample mean:
\[ \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \]
where \( x_i \) represents each individual speed and \( n \) is the total number of speeds.
2. Calculate the sample standard deviation:
\[ s = \sqrt{ \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1} } \]
3. Determine the standard error of the mean:
\[ SE = \frac{s}{\sqrt{n}} \]
4. Find the margin of error at 95% confidence level:
To find the margin of error, we use the t-distribution with degrees of freedom \( n-1 \) and a confidence level of 95%. We can look up the critical t-value in a t-table or use statistical software.
5. Calculate the confidence interval:
\[ \text{Confidence Interval} = \bar{x} \pm \text{Margin of Error} \]
Given the data provided on the speeds of 23 cars on Triphammer Road, we can compute the sample mean, standard deviation, standard error, and ultimately the 95% confidence interval for the mean speed of all cars on Triphammer Road. Remember to adjust the degrees of freedom in the t-distribution calculation based on the sample size.
