02: Explain randomization, replication, comparison, and control in experiments.

Given:

A scientist was hired to determine which brand of toothpaste is more effective in preventing cavities in children. Thirty children volunteered to participate in the experiment from which the scientist randomly created two groups of 15 children. The first group was given Brand A toothpaste, and the second group was given Brand B toothpaste. All of the children were given detailed directions describing when and how they should brush their teeth. After six months the children were taken to the same dentist and the number of cavities each child had was recorded. This data was used to determine which toothpaste is more effective.

Task:

1. Identify something the scientist tried to control in this experiment. Identify something the scientist did not consider controlling or was unable to control in this experiment and explain the adverse effects this might have had on the collected data.
2. Explain how replication was used in this experiment and why it is important.
3. The scientist randomly created the two groups. Instead, the scientist could have created the two groups based on some common characteristic, such as age or gender. Explain the adverse effects this might have had on this experiment.
4. Explain the role comparison plays in experiments and specify what was compared in this experiment.

08:

Task:

Write a brief essay in which you address the following:

1. Define "association" in statistics. Explain how association is identified and demonstrated.
2. Define "causation" in statistical analysis. Describe at least two factors that influence relationships between two variables and can lead to misinterpretation of data analysis.
3. Explain when it is appropriate to use averages when computing correlations. Explain what statisticians should be aware of when doing this.

12: Explain the Law of Large Numbers.

Task:

Write a brief essay ( suggested length of 2 pages ) in which you:

1. Define the Law of Large Numbers, citing a credible source.
2. Explain the Law of Large Numbers in your own words using a coin toss as an example.
3. Apply the Law of Large Numbers

1. Using a coin toss and fictitious data, explain how the following scenario is possible: As the number of trials increases, the differences between the number of actual and expected successes tends to grow, but the difference between the percentage of actual and expected successes tends to decrease.
2. Explain your answer to the following question: Is it true that if I flip a coin 1,000 times I will get heads 500 times?
3. Explain your answer to the following question: Is it true that if I get tails 3 times in a row that my chances of getting heads on my next toss is greater than 50%?

15: Explain why random samples are preferred.

Describe the advantages and limitations of commonly used sampling techniques.

Task:

Write a brief essay in which you:

1. Explain why random samples are preferred to nonrandom samples.
2. Describe the advantages and limitations of the following commonly used sampling techniques:

1. Simple random sampling
2. Stratified sampling
3. Cluster sampling
4. Multi-stage sampling

17: Construct simple hypothesis tests for means and proportions.

Given:

A potato chip company packages its potato chips into 12.0 ounce bags. You find it hard to believe that the bag contains enough potato chips to weigh 12.0 ounces and would like to make an official complaint. Before doing so, you decide to run an experiment so that you can have some confidence that the company’s claim is incorrect. Over the next several months you buy 30 bags of potato chips and weigh the contents of each one. You discover that the mean weight is 11.9 ounces with a standard deviation of 0.4 ounces. You decide that you will only complain if you can be 95% sure that the bags do not contain at least 12.0 ounces of potato chips. You decide to construct a hypothesis test.

Task:

1. Determine if this is a one-tailed or two-tailed test. Justify your decision.
2. State the null hypothesis and alternative hypothesis. Your null hypothesis should assume the company’s claim is correct.
3. Define the term Type I error and explain what a Type I error is in terms of this problem.
4. Define the term level of significance and identify the level of significance for this problem.
5. Calculate the test statistic as a z-score. Show all relevant work.
6. Using a standard table, you determine that the critical value is –1.645. Determine if you are able to reject the null hypothesis and explain how you reached this conclusion. ( Your conclusion should include a comment relating the results to the original problem. )

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Solution: The downloadable solution consists of 10 pages, 1766 words.
Deliverable: Word Document