Advanced Placement (AP) High School

For small sample sizes, an alternate method of constructing a confidence interval is available. To implement this method, first, include an additional 4 observations in the sample, 2 of which are successes and 2 of which are failures. Second, calculate a new sample proportion pˆnew for the new sample. Finally, construct a confidence interval using pˆnew , with the formula pˆnew±1. 96pˆnew(1−pˆnew)n+4−−−−−−−−−√.

(i) For the cell phone batteries, consider a sample of 5 in which 1 battery fails to last through 500 charges. Using the alternate method described, what is the value of pˆnew ? Show your work.

The following table shows the results of the original simulation with revised 95 percent confidence intervals constructed with the alternate method

Answers

Answer 1

The alternate method for constructing confidence intervals for small sample sizes involves adding four additional observations to the original sample, calculating a new sample proportion, and constructing a confidence interval using the new proportion and a modified formula. This method can improve the accuracy of the estimate of the population proportion, but should only be used for small sample sizes.

The alternate method for constructing confidence intervals for small sample sizes involves adding four additional observations to the original sample, two of which are successes and two of which are failures. This is done to increase the sample size and improve the accuracy of the estimate of the population proportion.Once the new sample has been created, the sample proportion pˆnew is calculated using the new sample. This proportion is then used to construct a confidence interval using the formula pˆnew±1. 96pˆnew(1−pˆnew)n+4−−−−−−−−−√. This formula takes into account the increased sample size and provides a more accurate estimate of the population proportion.The results of the original simulation can be compared with the revised 95 percent confidence intervals constructed using the alternate method. The revised intervals should be narrower and more accurate, since they are based on a larger sample size.It is important to note that the alternate method is only appropriate for small sample sizes. For larger sample sizes, the standard method of constructing confidence intervals should be used.

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Related Questions

A tablet charger uses 15 watts and it takes 5 hours to fully charge. The cost of electricity is $0.15/kWh. a. If this tablet is fully charged once a day. How many kWh does it use each year? (Remember to convert watts to kilowatts) b. What is the annual cost of charging this tablet?

Answers

Note that he annual cost of charging the tablet is approximately $4.11.

What is the explanation for the above response?


a. To calculate the kWh used each year, we first need to calculate the total energy used to fully charge the tablet once. Energy = Power x Time, so the energy used to charge the tablet once is:

Energy = 15 watts x 5 hours = 75 watt-hours (Wh)

To convert watt-hours to kilowatt-hours (kWh), we divide by 1,000:

75 Wh ÷ 1,000 = 0.075 kWh

So, the tablet uses 0.075 kWh of electricity to fully charge once. If it is charged once a day, it will use 0.075 kWh x 365 days = 27.375 kWh per year.

b. To calculate the annual cost of charging the tablet, we need to multiply the kWh used per year by the cost of electricity per kWh:

27.375 kWh x $0.15/kWh = $4.10625 per year

Therefore, the annual cost of charging the tablet is approximately $4.11.

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How do trade organizations (and supranational organizations) relate to economies of scale?

Answers

Trade organizations and supranational organizations can have a significant impact on economies of scale.

What is the trade?

Economies of scale refer to the cost advantages that arise when the production of goods or services is increased. As production volume increases, the average cost per unit decreases, leading to cost savings and increased efficiency.

Trade organizations, such as the World Trade Organization (WTO) or regional trade organizations like the European Union (EU), can facilitate economies of scale by promoting and regulating trade among member countries. By eliminating or reducing trade barriers, such as tariffs or quotas, trade organizations can facilitate increased trade volume among member countries. This increased trade volume can lead to economies of scale as producers can access larger markets and achieve higher production volumes, leading to lower costs per unit.

So, Supranational organizations, such as the EU, can also facilitate economies of scale by harmonizing regulations and standards among member countries.

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