A recent Gallup Poll asked 1523 adults if they bought a lottery ticket in the past year. Eight hundred sixty-eight (868) of the adults said “Yes.” The poll was carried out by telephone, so people without phones were excluded from the sample.

(a) Select the best answer to the question: Any errors in the final result due to excluding people without phones:

A) Are included in the announced margin of error.

B) Can be ignored, because these people are not part of the population.

C) Are in addition to the announced margin of error.

D) Can be ignored, because this is a nonsampling error.

**Selection:** A

(b) The _____________ that is estimated in this survey is the proportion *p* of all adults who bought a lottery ticket.

A) Mean

B) Confidence Interval

C) Parameter

D) Statistic

**Selection:** C

(c) Provide the sample proportion, p hat, used to estimate the population proportion *p* of all adults who bought a lottery ticket.

.57

(d) The value used to estimate the proportion *p* of all adults who bought a lottery ticket in the past year is called a __________.

A) Parameter

B) Statistic

C) Confidence Interval

D) Mean

**Selection:** C

(e) Find a 90% confidence interval for the population proportion *p* of all adults who bought a lottery ticket in the past year.

(.54906, .59079)

(f) Write a sentence interpreting your 90% confidence interval in the context of this problem.

We are 90% confident that the proportion of all adults who bought a lottery ticket in the past year are between .549 and .591

(g) An 80% confidence interval based upon this same sample would have:

A) The same center and a larger margin of error.

B) The same center and a smaller margin of error.

C) A larger margin of error and probably a different center.

D) A smaller margin of error and probably a different center.

E) The same center, but the margin of error changes randomly.

**Selection:** A

(h) A member of the Lottery Commission requests a 90% confidence interval estimate but with a smaller margin of error. How can we get a smaller margin of error using 90% confidence?

A) Take a smaller sample because smaller samples result in smaller margins of error.

B) Take a larger sample because larger samples result in smaller margins of error.

C) Take another sample of the same size because you might get lucky and get a smaller margin of error.

D) Take a sample of the same size from the adults in Ohio instead of the entire country. Then the population will be smaller and this will give a smaller margin of error.

**Selection:** B

Are all of these correct? Please be honest! If I’m wrong please correct me!

A recent Gallup Poll asked 1523 adults if they bought a lottery ticket in the past year. Eight hundred sixty-eight (868) of the adults said “Yes.” The poll was carried out by telephone, so people without phones were excluded from the sample.

Provide the sample proportion, p hat, used to estimate the population proportion p of all adults who bought a lottery ticket

(d) The value used to estimate the proportion *p* of all adults who bought a lottery ticket in the past year is called a?

(e) Find a 90% confidence interval for the population proportion *p* of all adults who bought a lottery ticket in the past year.

A recent Gallup Poll asked 1523 adults if they bought a lottery ticket in the past year. Eight hundred sixty-eight (868) of the adults said “Yes.” The poll was carried out by telephone, so people without phones were excluded from the sample.

(a) Select the best answer to the question: Any errors in the final result due to excluding people without phones:

A) Are included in the announced margin of error.

B) Can be ignored, because these people are not part of the population.

C) Are in addition to the announced margin of error.

D) Can be ignored, because this is a nonsampling error.

**Selection:**

(b) The _____________ that is estimated in this survey is the proportion *p* of all adults who bought a lottery ticket.

A) Mean

B) Confidence Interval

C) Parameter

D) Statistic

**Selection:**

(c) Provide the sample proportion, p hat, used to estimate the population proportion *p* of all adults who bought a lottery ticket.

(d) The value used to estimate the proportion *p* of all adults who bought a lottery ticket in the past year is called a __________.

A) Parameter

B) Statistic

C) Confidence Interval

D) Mean

**Selection:**

(e) Find a 90% confidence interval for the population proportion *p* of all adults who bought a lottery ticket in the past year.

(f) Write a sentence interpreting your 90% confidence interval in the context of this problem.

(d) The value used to estimate the proportion *p* of all adults who bought a lottery ticket in the past year is called a __________.

A) Parameter

B) Statistic

C) Confidence Interval

D) Mean

(a) Select the best answer to the question: Any errors in the final result due to excluding people without phones:

A) Are included in the announced margin of error.

B) Can be ignored, because these people are not part of the population.

C) Are in addition to the announced margin of error.

D) Can be ignored, because this is a nonsampling error.

**Selection:**

(b) The _____________ that is estimated in this survey is the proportion *p* of all adults who bought a lottery ticket.

A) Mean

B) Confidence Interval

C) Parameter

D) Statistic

**Selection:**

(c) Provide the sample proportion, p hat, used to estimate the population proportion *p* of all adults who bought a lottery ticket.

*p* of all adults who bought a lottery ticket in the past year is called a __________.

A) Parameter

B) Statistic

C) Confidence Interval

D) Mean

**Selection:**

*p* of all adults who bought a lottery ticket in the past year.

(f) Write a sentence interpreting your 90% confidence interval in the context of this problem.

(g) An 80% confidence interval based upon this same sample would have:

A) The same center and a larger margin of error.

B) The same center and a smaller margin of error.

C) A larger margin of error and probably a different center.

D) A smaller margin of error and probably a different center.

E) The same center, but the margin of error changes randomly.

h) A member of the Lottery Commission requests a 90% confidence interval estimate but with a smaller margin of error. How can we get a smaller margin of error using 90% confidence?

A) Take a smaller sample because smaller samples result in smaller margins of error.

B) Take a larger sample because larger samples result in smaller margins of error.

C) Take another sample of the same size because you might get lucky and get a smaller margin of error.

D) Take a sample of the same size from the adults in Ohio instead of the entire country. Then the population will be smaller and this will give a smaller margin of error.

1. Provide the sample proportion, p hat, used to estimate the population proportion *p* of all adults who bought a lottery ticket.

2. Find a 90% confidence interval for the population proportion *p* of all adults who bought a lottery ticket in the past year.

3. Write a sentence interpreting your 90% confidence interval in the context of this problem.

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