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#### 1)Explain the difference between descriptive and inferential statistics

###### Math

1)Explain the difference between descriptive and inferential statistics.

 2)
 Define a point estimate. What is the best point estimate for
 µ
 ?

1. Give two reasons the sample mean is the best point estimate for µ.
2. Define confidence interval and degree of confidence. Make up an example of a confidence
3. Define margin of error. Explain the relation between the confidence interval and the error estimate. Suppose a confidence interval is 9.65 < µ < 11.35. Find the sample mean x and the error estimate E.

1. Under what circumstances can you replace Η with s in the formula E = z ? /2 · Ηn .

1. How do you determine whether to use the z or t distribution in computing the margin of  , E = z ? /2 · Ηn or E = t?/2 · sn ?

distribution is required. Compute the error estimate using either E = z    /2 · Ηn or

 8)
 Describe the steps for finding a confidence interval.

1. When determining the sample size needed to achieve a particular error estimate you need               .
2. Explain how confidence intervals might be used to make decisions. Give an example to    clarify your explanation.
3. What assumption about the parent population is needed to use the t distribution to compute the margin of error?
4. Under what three conditions is it appropriate to use the t distribution in place of the standard normal distribution?
5. Interpret the following 95% confidence interval for mean weekly salaries of shift managers              at Guiseppe's Pizza and Pasta. 325.80 < µ < 472.30

 .
 14)
 Identify the correct distribution (z, t, or neither) for each of the following.
 15)
 15)
 Complete the table to compare z and t distributions.
 16
 What is the best point estimate for the population proportion? Explain why that point
 estimate is best.

1. Describe the process for finding the confidence interval for a population proportion.
1. When determining sample size we need to know p^. If we have no prior information, what  are two methods that can be used?
2. When determining the sample size for a desired margin of error, the formula is

z               /2 2 · p^ q^   . Based on this formula, discuss the fact that sample size is not n =               ?

E2 dependent on the population size; that is, it is not necessary to sample a particular percent of the population.

1. Why would manufacturers and businesses be interested in constructing a confidence interval for the population variance? Would manufacturers and businesses want large or small variances?
2. Draw a diagram of the chi- square distribution. Discuss its shape and values.

1. A radio show host asked people to call in and say whether they support new legislation to  promote cleaner sources of energy.  Based on this sample, she constructed a confidence interval to estimate the proportion of all listeners to her show who support the legislation. Is the confidence interval likely to give a good estimate of the proportion of her listeners who support the legislation?

1. Bert constructed a confidence interval to estimate the mean weight of students in his class.

The population was very small - only 30. Ruth constructed a confidence interval for the mean weight of all adult males in the city.  She based her confidence interval on a very small sample of only 5. Which confidence interval is likely to give a better estimate of the mean it is estimating? Which is likely to be more of a problem, a small sample or a small population?

1. A paper published the results of a poll. It stated that, based on a sample of 1000 married  men, 51% of married men say that they would marry the same woman again.  The margin of error was given as ±3  percentage points and the confidence level was given as 95%. What does it mean that the margin of error was ±3  percentage points?
2. Mark wanted to estimate the mean number of years of education of adults in his city. He  waited outside a public library and interviewed every tenth adult leaving.  Based on this sample, he constructed a confidence interval for the mean number of years of education of adults in the city. Do you think this confidence interval will give a good estimate? Why or why not?
3. Based on a simple random sample of students from her school, Sally obtained a point       estimate of the mean weight of students at her school. What additional information would be provided by a confidence interval estimate of the mean weight?
4. Hannah selected a simple random sample of all adults in her town and, based on this      sample,  constructed a confidence interval for the mean salary of all adults in the town. However, the distribution of salaries in the town is not exactly normal. Will the confidence interval still give a good estimate of the mean salary?

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