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Limitations and Alternatives to Random Sampling

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When is it possible to conduct random sampling, and when is it not? Give an example of a research question that might make random sampling really difficult? What is typically done in the field, given that random sampling is not always feasible (or sometimes, ethical)?

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When is it possible to conduct random sampling, and when is it not?

Answer: due to limited money and time, we often need to conduct a research by randomly picking up the sample from the whole population. When it is impossible to do the research on all the data, we have to use random sampling to collect data as a sample to be representative of the population.

However, ...

Solution Summary

The solution gives discussion on the use of random sampling, its limitation and its alternative. 270 words.

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Hypothesis Testing: Null and Alternative Hypotheses

1. Suppose you are trying to estimate the average miles per gallon for a new brand of car. You take a random sample of 40 cars, and, for this sample, the average miles per gallon is 32 and the standard deviation for this sample is 2.2. Answer the following questions in a Word document: •What is the population mean you are trying to estimate?
What value is the point estimate for the population mean? Describe, in your own words, what the point estimate represents.
Suppose you would like to construct a 90 percent confidence interval. What would be the margin of error for this interval?
What would be the lower and upper limits for this 90 percent confidence interval?
Now that you have constructed the interval, define its meaning in your own words.

2. You are trying to estimate the average amount that movie theaters charge for a large bucket of popcorn at theaters in the United States. Now, of course, you can't call up every single theater in the U.S. and ask them how much they charge for a large bucket of popcorn because that would take too much time. All you want is a good estimate, so you will create a confidence interval.
You randomly sample 50 theaters in the United States. You ask those theaters how much they charge for a large popcorn, and you get a sample mean of $6. Then, you create a confidence interval using this data with the lower limit at $4.50 and the upper limit at $7.50.
Explain why a confidence interval would or would not be appropriate in this example.
In your own words, interpret the meaning of this confidence interval.
If you only had a sample of 10 theaters instead of 50, would a confidence interval still be appropriate? Why or why not?
Describe a scenario where you could use the confidence interval in your daily life.

3. Suppose a car dealer tells you that specific cars get 35 miles per gallon on average. You would be able to use hypothesis tests to test whether or not this value might be correct. Why would you use a hypothesis test instead of a confidence interval in this situation?
A car dealer states that a new brand of car gets 35 miles per gallon on average. Suppose a consumer group claims that these cars get less than 35 miles per gallon. Set up the null and alternative hypotheses for this example.
The average daily rainfall in a jungle in South America was four inches back in 2000. Suppose a scientist thinks the average rainfall is different now. Set up the null and alternative hypotheses for this example.

4. A car dealer states that a new brand of car gets 35 miles per gallon on average. Suppose a consumer group claims that these cars get less than 35 miles per gallon. A sample of 40 cars is selected, and the sample mean for the 40 cars is 33 miles per gallon while the sample standard deviation is 3.8. •Have the assumptions for this test been met? Why or why not?
State the null and alternative hypothesis for this test.
Calculate the test statistic for this test. Explain what this test statistic represents.
Use technology to calculate the p-value for this test. Explain what this p-value represents.
State the conclusion for this test at the 0.05 level of significance. Do you think the car dealer is telling the truth? Why or why not?

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