# Lesson 14.B Questions

Lesson 14.B Questions

1) In a survey of 250 students on a college campus, 63% were getting financial aid. Complete the following sentence. Assume that the conditions of the Central Limit Theorem are satisfied. Express each limit to the nearest tenth.

We can be 95% confident that the true proportion of students who are getting financial aid is between ____________ and ___________.

(a) ...between 62.0% and 64.0%

(b) ...between 58.2% and 67.8%

(c) ...between 57.0% and 69.0%

(d) ...between 53.7% and 73.3%

2) In a poll of 200 randomly sampled children, 57% preferred ice cream to candy. What margin of error is required if we want to be 99.7% confident that our interval estimate contains the true proportion of children who prefer ice cream to candy?

a) ±10.4%

b) ±4.5%

c) ±7.0%

d) ±0.4%

Lesson 14.D Question

3) While some children are just naturally small, a doctor needs to monitor a child's growth. If the child is exceptionally small, the doctor looks at things like nutrition and family history to ensure if the child is healthy. The height of 18 month old boys is (roughly) normally distributed with a mean of 82 cm and a standard deviation of 3.3 cm. Should a doctor be concerned if an 18 month old boy is 75 cm? Why?

a) This child is small enough that a doctor should look more closely at the child's nutrition and family history.

b) This child is smaller than average, but not surprisingly so. The doctor should not be concerned.

c) The child is larger than average.

4) Based 2007 data from the CDC and National Vital Statistics System, a random simulation of 115 children’s deaths determined that 12 were due to cancer. Which of the following formulas will calculate

a 90% confidence interval to estimate the true proportion of children’s deaths due to cancer in 2007.

a) d)

b) e)

5) Based on data from 2005 to 2008 from the CDC and National Health and Nutrition Examination Survey, a random simulation of 157 women from age 65 to 74 found that 52 use statin medication to lower their cholesterol levels.

Part A: A 95% confidence interval for the true proportion of women from age 65 to 74 using statin medication from 2005 to 2008 is desired. Check the conditions for inference.

The z-score that matches a 95% confidence level is ________

p ^= q ^=

Part B: Calculate and interpret the confidence interval stated in part (a).

CI = ( ______ , _______ ) Round each number to 4 decimal places

Interpretation: We are ____% confident that the true proportion of women from age ___ to ___ using statin medication from 2005 to 2008 is between _______ % and ________ %.

6) Fracking is a process of drilling and injecting fluid into the ground at high pressures to fracture shale rocks and release natural gas inside. According to a Gallup Poll in early March, 2015, the highest proportion of Americans that favor fracking are those who are 65 years or older. Suppose a random survey of 255 Americans older than 65 discovered that 141 are in favor of fracking. Which of the following is the correct 90% confidence interval and interpretation of the confidence level?

(.502, .604) In repeated samples, this method will capture the true proportion of Americans over 65 years old that are in favor of fracking.

(.502, .604) We are 90% confidence that the true proportion of Americans over 65 years old that are in favor of fracking lies between .502 and .604.

(.491, .614) In repeated samples, this method will capture the true proportion of Americans over 65 years old that are in favor of fracking.

(.491, .614) We are 90% confidence that the true proportion of Americans over 65 years old that are in favor of fracking lies between .491 and .614.

(.491, .614) In the long run, this method will produce the interval .491 and .614 in about 90% of all samples.

Do half of Americans oppose college athlete unions? An ABC News/Washington Post Poll conducted in March of 2014 of 1,002 American adults found that 471 opposed college athletes being able to form a union, like the professional sports, to negotiate their rights and working conditions.

Is there enough evidence to believe that less than half of American adults oppose the college athlete unions? The p-value calculated from this scenario is 0.029. Using a level of significance of 5%, which of the following conclusions is correct?

We reject Ho, since the p-value < a, there is enough evidence to believe that half of Americans

oppose college athletes being able to form unions.

We reject Ho, since the p-value < a, there is enough evidence to believe that less than half of American adults oppose college athletes being able to form unions.

We fail to reject Ho, since the p-value < a, there is enough evidence to believe that less than half of American adults oppose college athletes being able to form unions.

We fail to reject Ho, since the p-value < a, there is not enough evidence to believe that less than half of American adults oppose college athletes being able to form unions.

We fail to reject Ho, since the p-value < a, there is enough evidence to believe that half of American adults oppose college athletes being able to form unions.

Some books on Amazon.com have more than 20,000 reviews written voicing people’s opinions on the book. Do all top selling books have thousands of reviews? Suppose we suspect that less than

half of the top selling books in the Amazon Kindle store have less than 10% of this lofty total (2,000 reviews).

Suppose that a systematic random sample of the 200 best-selling books at the Amazon Kindle store in March of 2015 found that 10 of the 25 e-books had less than 2,000 reviews. Which of the following displays the correct formula of the z-score needed to run a proportion z-?

A Gallup Poll conducted in November 2014 asked the question, “Thinking about your weight, how would you describe your own personal weight situation right now:

very overweight,

somewhat overweight,

about right,

somewhat underweight, or

very underweight?”

Of the 828 adults nationwide surveyed, 464 responded “about right.”

Using the 5-steps for hypothesis ing, determine if there is sufficient evidence to believe over 50% of adults believe their weight is “about right.”

H0 : __________

HA : __________

np = _______________ nq = _____________

This means the sample size is ______________________.

Is the sample size less than 10% of the population? ______

The p-value corresponding to this z-score is _________

What is your decision based upon using a significance level of a = 0.05 ?

(Include the 3 parts of the decision: Your decision about H0, your evaluation of the p-value vs the significance level, and your evaluation of the claim – as outlined in Lesson 16C)

1) In a survey of 250 students on a college campus, 63% were getting financial aid. Complete the following sentence. Assume that the conditions of the Central Limit Theorem are satisfied. Express each limit to the nearest tenth.

We can be 95% confident that the true proportion of students who are getting financial aid is between ____________ and ___________.

(a) ...between 62.0% and 64.0%

(b) ...between 58.2% and 67.8%

(c) ...between 57.0% and 69.0%

(d) ...between 53.7% and 73.3%

2) In a poll of 200 randomly sampled children, 57% preferred ice cream to candy. What margin of error is required if we want to be 99.7% confident that our interval estimate contains the true proportion of children who prefer ice cream to candy?

a) ±10.4%

b) ±4.5%

c) ±7.0%

d) ±0.4%

Lesson 14.D Question

3) While some children are just naturally small, a doctor needs to monitor a child's growth. If the child is exceptionally small, the doctor looks at things like nutrition and family history to ensure if the child is healthy. The height of 18 month old boys is (roughly) normally distributed with a mean of 82 cm and a standard deviation of 3.3 cm. Should a doctor be concerned if an 18 month old boy is 75 cm? Why?

a) This child is small enough that a doctor should look more closely at the child's nutrition and family history.

b) This child is smaller than average, but not surprisingly so. The doctor should not be concerned.

c) The child is larger than average.

4) Based 2007 data from the CDC and National Vital Statistics System, a random simulation of 115 children’s deaths determined that 12 were due to cancer. Which of the following formulas will calculate

a 90% confidence interval to estimate the true proportion of children’s deaths due to cancer in 2007.

a) d)

b) e)

5) Based on data from 2005 to 2008 from the CDC and National Health and Nutrition Examination Survey, a random simulation of 157 women from age 65 to 74 found that 52 use statin medication to lower their cholesterol levels.

Part A: A 95% confidence interval for the true proportion of women from age 65 to 74 using statin medication from 2005 to 2008 is desired. Check the conditions for inference.

The z-score that matches a 95% confidence level is ________

p ^= q ^=

Part B: Calculate and interpret the confidence interval stated in part (a).

CI = ( ______ , _______ ) Round each number to 4 decimal places

Interpretation: We are ____% confident that the true proportion of women from age ___ to ___ using statin medication from 2005 to 2008 is between _______ % and ________ %.

6) Fracking is a process of drilling and injecting fluid into the ground at high pressures to fracture shale rocks and release natural gas inside. According to a Gallup Poll in early March, 2015, the highest proportion of Americans that favor fracking are those who are 65 years or older. Suppose a random survey of 255 Americans older than 65 discovered that 141 are in favor of fracking. Which of the following is the correct 90% confidence interval and interpretation of the confidence level?

(.502, .604) In repeated samples, this method will capture the true proportion of Americans over 65 years old that are in favor of fracking.

(.502, .604) We are 90% confidence that the true proportion of Americans over 65 years old that are in favor of fracking lies between .502 and .604.

(.491, .614) In repeated samples, this method will capture the true proportion of Americans over 65 years old that are in favor of fracking.

(.491, .614) We are 90% confidence that the true proportion of Americans over 65 years old that are in favor of fracking lies between .491 and .614.

(.491, .614) In the long run, this method will produce the interval .491 and .614 in about 90% of all samples.

Do half of Americans oppose college athlete unions? An ABC News/Washington Post Poll conducted in March of 2014 of 1,002 American adults found that 471 opposed college athletes being able to form a union, like the professional sports, to negotiate their rights and working conditions.

Is there enough evidence to believe that less than half of American adults oppose the college athlete unions? The p-value calculated from this scenario is 0.029. Using a level of significance of 5%, which of the following conclusions is correct?

We reject Ho, since the p-value < a, there is enough evidence to believe that half of Americans

oppose college athletes being able to form unions.

We reject Ho, since the p-value < a, there is enough evidence to believe that less than half of American adults oppose college athletes being able to form unions.

We fail to reject Ho, since the p-value < a, there is enough evidence to believe that less than half of American adults oppose college athletes being able to form unions.

We fail to reject Ho, since the p-value < a, there is not enough evidence to believe that less than half of American adults oppose college athletes being able to form unions.

We fail to reject Ho, since the p-value < a, there is enough evidence to believe that half of American adults oppose college athletes being able to form unions.

Some books on Amazon.com have more than 20,000 reviews written voicing people’s opinions on the book. Do all top selling books have thousands of reviews? Suppose we suspect that less than

half of the top selling books in the Amazon Kindle store have less than 10% of this lofty total (2,000 reviews).

Suppose that a systematic random sample of the 200 best-selling books at the Amazon Kindle store in March of 2015 found that 10 of the 25 e-books had less than 2,000 reviews. Which of the following displays the correct formula of the z-score needed to run a proportion z-?

A Gallup Poll conducted in November 2014 asked the question, “Thinking about your weight, how would you describe your own personal weight situation right now:

very overweight,

somewhat overweight,

about right,

somewhat underweight, or

very underweight?”

Of the 828 adults nationwide surveyed, 464 responded “about right.”

Using the 5-steps for hypothesis ing, determine if there is sufficient evidence to believe over 50% of adults believe their weight is “about right.”

H0 : __________

HA : __________

np = _______________ nq = _____________

This means the sample size is ______________________.

Is the sample size less than 10% of the population? ______

The p-value corresponding to this z-score is _________

What is your decision based upon using a significance level of a = 0.05 ?

(Include the 3 parts of the decision: Your decision about H0, your evaluation of the p-value vs the significance level, and your evaluation of the claim – as outlined in Lesson 16C)

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