Suppose that, in a suburb of 12,529 people, 6,565 people moved there within the last five years. You survey 550 and find that 257 of the people in your sample moved to the suburb in the last five years.

a. What is the population proportion of people who moved to the suburb in the last five years?

The population proportion is

(Round to the nearest thousandth as needed.)

b. What is the sample proportion of people who moved to the suburb in the last five years?

The sample proportion is

(Round to the nearest thousandth as needed.)

c. Does your sample appear to be representative of the population? Yes? Or No?

2.)
You select a random sample of 180 people at a medical convention attended by 1,763 people. Within your sample, you find that 76 people have traveled from abroad. Based on this sample statistic, estimate how many people at the convention traveled from abroad. Would you be more confident of your estimate if you sampled 300 people?

The number of people at the convention traveled from abroad is

(Round to he nearest whole number as needed.)

Would you be more confident of your estimate if you sampled 300 people?

Yes

No

3.)

List the different possible samples and find the mean of each of them. Select the correct choice below and fill in the answer boxes within your choice.

A.

Sample

Mean x

10-10

10-8

10-3

8-10

8-8

8-3

3-10

3-8

3-3

B.

Sample

Mean x

10-10

10-8

10-3

8-8

8-3

3-3

C.

Sample

Mean x

10-8

10-3

8-10

8-3

3-10

3-8

D.

Sample

Mean x

10-8

10-3

8-3

b. Identify the probability of each sample and describe the sampling distribution of sample means.

Each sample has probability
(Type an integer or a simplified fraction.)

To describe the sampling distribution of sample means, complete the table below.

x

Probability

10

9

8

6.5

5.5

3

(Type an integer or a fraction. Do not simplify.)

c. Find the mean of the sampling distribution.

μ =
(Type an integer or decimal rounded to two decimal places as needed.)

d. Is the mean of the sampling distribution [from part (c)] equal to the mean of the population of the three listed values? If so, are those means always equal?

A.

No, the sample mean is not equal to the mean of the population. These means are not always equal, because the mean is an unbiased estimator.

B.

Yes, the sample mean is equal to the mean of the population. These means are always equal, because the mean is an unbiased estimator.

C.

Yes, the sample mean is equal to the mean of the population. These means are always equal, because the mean is a biased estimator.

D.

No, the sample mean is not equal to the mean of the population. These means are not always equal, because the mean is a biased estimator.

5.)

Here is a typical statement made by the media: “Based on a recent study, pennies weigh an average of 2.5 grams with a margin of error of 0.006 gram.” What important and relevant piece of information is omitted from that statement? Is it OK to use the word “average”?

Choose the correct answer below.

A.

The media often omit reference to the confidence interval. The word “mean” should be used instead of the word “average.”

B.

The media often omit reference to the confidence level, which is typically 95%. It is OK to use the word “average” in this context.

C.

The media often omit reference to the confidence level, which is typically 95%. The word “mean” should be used instead of the word “average.”

D.

The media often omit reference to the confidence interval. It is OK to use the word “average” in this context.

6)

Assume that population means are to be estimated from the samples described. Use the sample results to approximate the margin of error and 95% confidence interval.

Sample size= 1,030 , Sample mean = $46,254

The margin of error is

$

(Round to the nearest dollar as needed.)

Find the 95% confidence interval.

$
< μ < $ nothing (Round to the nearest dollar as needed.) 7.) One researcher wishes to estimate the mean number of hours that high school students spend watching TV on a weekday. A margin of error of 0.25 hour is desired. Past studies suggest that a population standard deviation of 1.5 hours is reasonable. Estimate the minimum sample size required to estimate the population mean with the stated accuracy. The required sample size is (Round up to the nearest whole number.) 8.) You want to estimate the mean weight of quarters in circulation. A sample of 50 quarters has a mean weight of 5.656 grams and a standard deviation of 0.063 gram. Use a single value to estimate the mean weight of all quarters. Also, find the 95% confidence interval for the average weight of all quarters. The mean weight of all quarters is approximately grams. (Round to the nearest thousandth as needed.) Find the 95% confidence interval for the average weight of all quarters. g < μ < g (Round to the nearest thousandth as needed.) 9) Assume the population proportion is to be estimated from the sample described. Find the approximate margin of error and the 95% confidence interval for the population proportion. Sample size = 256, Sample proportion = 0.28 The margin of error is (Round to four decimal places as needed.) Find the 95% confidence interval. < p < (Round to the three decimal places as needed.) 10.) Estimate the minimum sample size needed to achieve the margin of error =0.197 The minimum sample size is (Round up to the nearest integer.) 11.) A study done by researchers at a university concluded that 70% of all student athletes in this country have been subjected to some form of hazing. The study is based on responses from 1,700 athletes. What are the margin of error and 95% confidence interval for the study? The margin of error is (Round to the nearest thousandth as needed.) Find the 95% confidence interval. < p < (Round to the nearest thousandth as needed.) 12.) A research poll included 1,800 randomly selected adults who were asked whether "global warming is a problem that requires immediate government action." Results showed that 994 of those surveyed indicated that immediate government action is required. A news reporter wants to determine whether these survey results constitute strong evidence that the majority (more than 50%) of people believe that immediate government action is required. Complete parts (a) through (c) below. a. What is the best estimate of the proportion of adults who believe that immediate government action is required? ^p = (Round to three decimal places as needed.) b. Construct a 95% confidence interval estimate of the proportion of adults believing that immediate government action is required. <p < (Round to three decimal places as needed.) c. Is there strong evidence supporting the claim that the majority is in favor of immediate government action? Why or why not? A. Yes. Because the sample proportion, ^p is greater than 0.5, it does appear that the majority (more than 50%) is in favor of immediate government action. B. Yes. Because the range of values in the confidence interval includes only values greater than 0.5, it does appear that the majority (more than 50%) is in favor of immediate government action. C. No. Because the range of values in the confidence interval is greater than two standard deviations, it does not appear that the majority (more than 50%) is in favor of immediate government action. D. No. There is not enough evidence to support the claim that the majority (more than 50%) is in favor of immediate government action.

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