AskSia

Plus

Class exercise: Market Summary > Dow Jones Industrial Average 41,175.08 + Follo...

Aug 26, 2024

Solution by Steps

For Question 1: 90% Confidence Interval for the DJA at 5pm, Sept. 30, 2024

step 1

To calculate the 90% confidence interval, we need to determine the mean and standard deviation of the DJA values over the specified period. Assuming a normal distribution, we can use the formula for the confidence interval:

CI = \bar{x} \pm z \cdot \frac{\sigma}{\sqrt{n}}

where

z

is the z-score corresponding to 90% confidence level

step 2

For a 90% confidence level, the z-score is approximately 1.645. We will need the mean

\bar{x}

and standard deviation

\sigma

of the DJA values to compute the interval

step 3

Assuming we have the mean and standard deviation, we can plug in the values to find the low (5%) and high (95%) percentiles. The low (5%) and high (95%) values can be calculated as:

Low(5\%) = \bar{x} - 1.645 \cdot \frac{\sigma}{\sqrt{n}}

and

Hi(95\%) = \bar{x} + 1.645 \cdot \frac{\sigma}{\sqrt{n}}

. The median will be the same as the mean in a normal distribution

Answer

Low(5%) = ____, Median = ____, Hi(95%) = ____

--- For Question 2: Ratio of Total Tonnage of US CO2 Emissions to China's Total CO2 Emissions

step 1

To find the ratio of total tonnage of US CO2 emissions to China's total CO2 emissions, we need the total emissions data for both countries. The ratio can be calculated as:

Ratio = \frac{US\ CO2\ emissions}{China\ CO2\ emissions}

step 2

To compute the confidence interval for this ratio, we can use the delta method or bootstrap methods to estimate the standard error of the ratio. The confidence interval can be calculated similarly to the first question

step 3

Assuming we have the necessary data, we can calculate the low (5%) and high (95%) percentiles for the ratio using the same z-score method as before

Answer

Low(5%) = ____, Median = ____, Hi(95%) = ____

--- For Question 3: Ratio of Per Capita US CO2 Emissions to China's Per Capita Emissions

step 1

To find the ratio of per capita US CO2 emissions to China's per capita emissions, we need the per capita emissions data for both countries. The ratio can be calculated as:

Ratio = \frac{US\ per\ capita\ CO2\ emissions}{China\ per\ capita\ CO2\ emissions}

step 2

To compute the confidence interval for this ratio, we can again use the delta method or bootstrap methods to estimate the standard error of the ratio. The confidence interval can be calculated similarly to the previous questions

step 3

Assuming we have the necessary data, we can calculate the low (5%) and high (95%) percentiles for the ratio using the same z-score method as before. The width of the confidence interval can be calculated as:

Width = Hi(95\%) - Low(5\%)

Answer

Low(5%) = ____, Median = ____, Hi(95%) = ____, Width = ____

Key Concept

Confidence intervals provide a range of values that likely contain the population parameter.

Explanation

The answers require data to compute specific values for the confidence intervals and ratios, which can be derived from statistical methods.