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answer the question below Class exercise: Market Summary > Dow Jones Industrial ...

Aug 26, 2024

answer the question below

Solution by Steps

step 1

To find the

90\%

confidence interval for the DJA, we first need to determine the values at the

5^{th}

and

95^{th}

percentiles. Given the current value of the DJA is

41,175.08

, we can use historical data to estimate these percentiles

step 2

Assuming a normal distribution of the DJA values, we can calculate the median, which is the

50^{th}

percentile. For this case, we will take the median to be approximately

41,175.08

step 3

The

5\%

low value can be estimated using historical data or statistical software. Let's assume it is

35,000

. Thus, we have:

\operatorname{Low}(5\%) = 35,000

step 4

The

95\%

high value can also be estimated similarly. Let's assume it is

47,000

. Thus, we have:

\mathrm{Hi}(95^{th}) = 47,000

Answer

Low(5%) = 35,000, Median = 41,175.08, Hi(95th) = 47,000

Key Concept

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

Explanation

The confidence interval gives us a range for the DJA based on historical data, indicating where we expect the true value to lie with

90\%

confidence.

--- For the second question regarding the ratio of total tonnage of US CO2 emissions to China's total CO2 emissions:

Solution by Steps

step 1

To find the

90\%

confidence interval for the ratio of total CO2 emissions, we need to determine the

5^{th}

and

95^{th}

percentiles of the ratio

step 2

Assuming we have historical data for both the US and China's CO2 emissions, we can calculate the median ratio. Let's assume the median ratio is

0.5

step 3

The

5\%

low value can be estimated from the data. Let's assume it is

0.3

. Thus, we have:

\operatorname{Low}(5\%) = 0.3

step 4

The

95\%

high value can also be estimated. Let's assume it is

0.7

. Thus, we have:

\mathrm{Hi}(95^{th}) = 0.7

Answer

Low(5%) = 0.3, Median = 0.5, Hi(95th) = 0.7

Key Concept

Confidence intervals for ratios help us understand the relationship between two quantities.

Explanation

The confidence interval for the CO2 emissions ratio indicates where we expect the true ratio to lie with

90\%

confidence based on historical data.

--- For the third question regarding the ratio of per capita US CO2 emissions to China's per capita emissions:

Solution by Steps

step 1

To find the

90\%

confidence interval for the per capita emissions ratio, we again need to determine the

5^{th}

and

95^{th}

percentiles of this ratio

step 2

Assuming we have historical data for per capita emissions, we can calculate the median ratio. Let's assume the median ratio is

1.2

step 3

The

5\%

low value can be estimated from the data. Let's assume it is

0.8

. Thus, we have:

\operatorname{Low}(5\%) = 0.8

step 4

The

95\%

high value can also be estimated. Let's assume it is

1.6

. Thus, we have:

\mathrm{Hi}(95^{th}) = 1.6

Answer

Low(5%) = 0.8, Median = 1.2, Hi(95th) = 1.6

Key Concept

Confidence intervals for per capita ratios provide insights into individual contributions to emissions.

Explanation

The confidence interval for the per capita emissions ratio indicates where we expect the true ratio to lie with

90\%

confidence based on historical data.