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# The importance of sampling

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Why is sampling so important? Some people have argued that sampling is not beneficial, because important aspects of the population may be omitted. Do you agree or disagree with that line of thinking?

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Question) Why is sampling so important?
Answer) Sampling is important because it gives us an idea of what is happening in the population. The sample represents the population as a whole, and from the sample, we can make conclusions about the population. Of course, it is best if the entire population can be surveyed, but this is often costly and time-prohibitive. In contrast, sampling is much cheaper, and faster, and more practical. Since sampling takes less time and money, researchers can conduct sampling for many different research topics. For the same amount of time and money, only a small number of research topics would be explored if the entire population were surveyed. Sampling is a good ...

#### Solution Summary

The solution contains over 400 words of text explaining the importance of sampling, why it could be better than surveying a population, and how to decrease the likelihood that the sample is not indicative of the population.

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## Importance of Pooled Variance

1. What is pooled variance and why is it important?

2. Explain what interval data is and give an example:

3. Write the formula for a problem that has 2 sample populations greater than 30 and the standard deviations are known and equal:

4. Write the formula for pooled variance.

5. Please analyze the following data:

A school district wants to determine if the girls are equal to boys in test scores. They took a random sample of 22 8th grade girls and 24 8th grade boys. The district looked at recent CAT scores and found the mean score for girls to be xbar1 = 25 and the mean score for boys to be xbar2 = 26. The standard deviation for the girls is s1 = 2.2 and for the boys the standard deviation is s2 = 3.4. Is the school district correct in assuming the girls are equal in performance to boys. They are 95% sure their assumption is correct.

6. Please analyze the following data

A candy company wants to identify whether or not the size of its' candy bars are the same length from one day to another. On day 1 they sample 52 candy bars with an average mean of 5.4 inches and on day 2 they sample 52 bars again with and average mean of 5.6 inches. Both days have sample standard deviations of 3.4. Is the average mean of size different from day 1 to day 2?

7. A sample of 40 observations is selected from one population. The sample mean is 102 and the sample standard deviation is 5. A sample of 50 observations is selected from a second population. The sample mean is 99 and the sample standard deviation is 6. Conduct the following test using 95% level of confidence.
A. Is it a 1 or 2 tail test
B. Compute the statistical calculation
C. What is your decision regarding H1

8. A sample of 65 observations is selected from one population. The sample mean is 2.67 and the sample standard deviation is .75. A sample of 50 observations is selected from a second population. The sample mean is 2.59 and the sample standard deviation is .66. Conduct the following test using 95% level of confidence.
a. Is it a 1 or 2 tail tes
b. Compute the statistical calculation
c. What is your decision regarding H1

9. The Gibbs Baby Food Company wishes to compare the weight gain of infants using their brand versus their competitor's brand. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first 3 months after birth. The standard deviation of this sample is 2.3 pounds. A sample of 55 babies using the competitors brand revealed a mean increase of 8.8 pounds with a standard deviation of 2.9 pounds. At 95% level of confidence, can we conclude that the babies using the Gibbs product gained LESS weight?

10. What key words tell you that the Hypothesis is to be set up as a 1 Tail UPPER?

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