Using this information, calculate two 95% confidence intervals. For the first interval you need to calculate a T-confidence interval for the sample population. You have the mean, standard deviation and the sample size, all you have left to find is the T-critical value and you can calculate the interval. For the second interval calculate a proportion confidence interval using the proportion of the number of cars that fall below the average. You have the p, q, and n, all that is left is calculating a Z-critical value,

QUESTION

Using the data set you collected in Week 1, excluding the super car outlier, you should have calculated the mean and standard deviation during Week 2 for price data. Along with finding a p and q from Week 3. Using this information, calculate two 95% confidence intervals. For the first interval you need to calculate a T-confidence interval for the sample population. You have the mean, standard deviation and the sample size, all you have left to find is the T-critical value and you can calculate the interval. For the second interval calculate a proportion confidence interval using the proportion of the number of cars that fall below the average. You have the p, q, and n, all that is left is calculating a Z-critical value,

Make sure you include these values in your post, so your fellow classmates can use them to calculate their own confidence intervals. Once you calculate the confidence intervals you will need to interpret your interval and explain what this means in words.

Do the confidence intervals surprise you, knowing what you have learned about confidence intervals, proportions and normal distribution? Please the Week 5 Confidence T-Interval Mean and Unknown SD PDF and the Week 5 Confidence Interval Proportions PDF at the bottom of the discussion forum. This will give you a step by step example on how to help you calculate this using Excel. These PDFs will also help you in Tests&Quizzes tab.

Instructions: Your initial post should be at least 150 words.

WEEK 1 DATA:

STATISTICS

ANSWER

To calculate the confidence intervals, we need to use the data set collected in Week 1, excluding the supercar outlier. Let’s summarize the data we have:

Mean: $26,194.67
Standard Deviation: $6,430.06
Sample Size: 10

For the T-confidence interval, we will use a 95% confidence level. Since the sample size is small (<30) and the population standard deviation is unknown, we will use the t-distribution. The critical value can be obtained from the t-distribution table or by using statistical software. With a sample size of 10 and a desired confidence level of 95%, the T-critical value is approximately 2.262.

Using this information, we can calculate the T-confidence interval:

T-confidence interval = Mean ± (T-critical value * Standard Deviation / √n)
= $26,194.67 ± (2.262 * $6,430.06 / √10)
= $26,194.67 ± $4,541.50

This yields a T-confidence interval of ($21,653.17, $30,736.17). This means that we are 95% confident that the true population mean falls within this range.

For the proportion confidence interval, we will calculate the proportion of cars that fall below the average. The proportion (p) can be calculated as the number of cars below the mean divided by the sample size (n). In this case, there are 6 cars below the mean, so p = 6/10 = 0.6. The complement of p (q) is equal to 1 – p, which is 0.4.

To calculate the Z-critical value, we can use a Z-table or statistical software. For a 95% confidence level, the Z-critical value is approximately 1.96.

Using these values, we can calculate the proportion confidence interval:

Proportion confidence interval = p ± (Z-critical value * √(p*q/n))
= 0.6 ± (1.96 * √(0.6*0.4/10))
= 0.6 ± 0.491

This yields a proportion confidence interval of (0.109, 1.091). This means that we are 95% confident that the proportion of cars below the average falls within this range.

Given the small sample size and the data collected, the confidence intervals obtained are reasonable. The T-confidence interval for the sample population provides a range within which we can be 95% confident that the true population mean lies. The proportion confidence interval gives us a range for the proportion of cars below the average. These intervals allow us to make statistical inferences about the population based on our sample data.