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Question 1 Select one answer. 10 points In a Fox News Poll conducted in October 2011, 904 registered voters nationwide answered the following question: “Do you think illegal immigrants who have lived in the United States since they were children should be eligible for legal citizenship, or not?” 63% answered “should be” eligible for legal citizenship with a margin of error of 3% at a 95% level of confidence. Which of the following statements is correct? • We are 95% confident that between 57% and 69% of all registered voters nationwide will answer illegal immigrants “should be” eligible for legal citizenship. • We are 95% confident that between 60% and 66% of all registered voters nationwide will answer illegal immigrants “should be” eligible for legal citizenship. • We are 95% confident that 63% of the 904 registered voters in the sample answered illegal immigrants “should be” eligible for legal citizenship.” • We are confident that 95% of the 904 registered voters in the sample answered “should be.” Question 2 Select one answer. 10 points Living at home: According to a 2011 report from the U.S. Census, 59% of young men (age 18-24) are living at home with their parents. Suppose that we plan to select a random sample of 100 young men from your community. If we use the national figure of 59%, we estimate that the standard error is about 0.05 for results from random samples of 100 young men from your community. When we select a random sample of 100 young men from your community, we find that 50% are living at home. Which gives the best interpretation of the 95% confidence interval to estimate the percentage of young men in your community who are living at home? • We are 95% confident that 50% of the young men in your community are living at home. • We are 95% confident that 45% to 55% of the young men in your community are living at home. • We are 95% confident that 40% to 60% of the young men in your community are living at home. Question 3 Select one answer. 10 points Academic advising: In 2014 the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. In a simulation we select random samples from this population. For each sample we calculate the proportion who rarely or never use academic advising services. What is the smallest sample in the list below that will satisfy the conditions for the use of a normal model to represent the sampling distribution? • 15 • 20 • 25 • 30 Question 4 Select one answer. 10 points There are over 3 million students enrolled in community colleges in the U.S. A total of 443,818 students at 699 community colleges completed the Community College Survey of Student Engagement (CCSSE) between 2009 and 2011. About half (50%) of students reported that they “often” or “very often” prepare two or more drafts of a paper before turning it in. True or false? The 50% is a statistic representing a sample of 443,818 community college students. • True • False Question 5 Type numbers in the boxes. Part 1: 10 points Part 2: 10 points 20 points Academic advising: In 2014, the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. In a simulation we select random samples from this population. For each sample we calculate the proportion who rarely or never use academic advising services. If we repeatedly obtain random samples of 200 students, what will be the mean and standard deviation of the sampling distribution of sample proportions? Mean (round to 2 decimal places AFTER completing all calculations): Standard deviation (round to 3 decimal places AFTER completing all calculations): Question 6 Select one answer. 10 points Orange M&M’s: The M&M’s web site says that 20% of milk chocolate M&M’s are orange. Let’s assume this is true and set up a simulation to mimic buying 200 small bags of milk chocolate M&M’s. Each bag contains 55 candies. We made this dotplot of the results. Now suppose that we buy a small bag of M&M’s. We find that 25.5% (14 of the 55) of the M&M’s are orange. What can we conclude? • This result is not surprising because we expect to see many samples with 14 or more orange candies. • This result is surprising because it is unlikely that we will select a random sample with 25.5% or more orange candies if 20% of milk chocolate M&M’s are orange. • This result is surprising because we expect the orange candies to make up no more than 20% of the candies in a packet. Question 7 Select one answer. 10 points Orange M&M’s: The M&M’s web site says that 20% of milk chocolate M&M’s are orange. Let’s assume this is true and set up a simulation to mimic buying 200 small bags of milk chocolate M&M’s. Each bag contains 55 candies. We made this dotplot of the results. The number of orange M&M’s was counted and here is a dotplot of the results: Which of the following reasons best explains the variability we see in the proportion of orange M&M’s in the bags? • Poor quality control in the production process • Human error in calculating the proportion of orange M&M’s in a bag • An error in the simulation • The random selection of samples Question 8 Select one answer. 10 points Academic advising: In 2014, the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. In a simulation we select random samples from this population. For each sample we calculate the proportion who rarely or never use academic advising services. If we randomly sample 200 students from this population repeatedly, the standard error is approximately 3.5%. Is it unusual to see 32% who rarely or never use academic advising services in one of these samples? • Yes, this is unusual because 32% is 2.9 standard errors below 42%. It is very rare for a sample to be nearly three standard errors from the mean. • Yes, this is unusual because 32% is 10% lower than 42%. • No, this is unusual because the error is only 10%. • No, this is unusual because 32% is 2.9 standard errors below 42%. Question 9 Select one answer. 10 points STD study: A 2008 CDC study estimated that 26% of young women between the ages of 14 and 19 in the U.S. were infected with at least one of the most common sexually transmitted diseases (human papillomavirus [HPV]), chlamydia, herpes simplex virus, and trichomoniasis). Is the percentage lower in your community? Suppose that we select a random sample of 100 young women in your community. We can use a normal model for the sampling distribution because the conditions are met. We expect 26 of the 100 to be infected with at least one of the most common STDs and 74 to not be infected. So we can find the Z-score and use the applet to assess the evidence provided by the data. (The standard error is about 0.044.) Here is a link to the applet. Suppose that in a random sample of 100 young women in your community, 20% are infected with at least one of the most common STDs True or false? We can conclude that the percentage of all young women in your community who are infected with at least one of the most common STDs is less than 26%. • True • False Question 10 Select one answer. 10 points Living at Home: According to a 2011 report from the U.S. Census, 59% of young men (age 18-24) are living at home with their parents. Is the percentage higher in your community? Suppose that we select a random sample of 20 young men from your community. We cannot use a normal model for the sampling distribution because one of the conditions is not met since n(1–p) is not 10 or greater. We expect 41% of the young men are not living with their parents. This is 0.41(20) = 8.2. So we ran a simulation with p = 0.59 and n = 20. Suppose that the sample of 20 young men from your community has 14 living at home. This is 70% of the sample. Do the data suggest that the percentage of young men living at home in your community is higher than 59%? • Yes, because 70% is an error of 11%. • Yes, because it is unlikely that 70% or more will be living at home in a sample of 20 young men given the population percentage is 59%. • No, because it is not surprising to see 70% or more living at home in a sample of 20 young men if 59% of all young men in the community live at home. • No, because we expect results from random samples to vary. So 70% is not surprising.

Question 1

Select one answer.

10 points

In a Fox News Poll conducted in October 2011, 904 registered voters nationwide answered the following question: “Do you think illegal immigrants who have lived in the United States since they were children should be eligible for legal citizenship, or not?” 63% answered “should be” eligible for legal citizenship with a margin of error of 3% at a 95% level of confidence.

Which of the following statements is correct?

  •  We are 95% confident that between 57% and 69% of all registered voters nationwide will answer illegal immigrants “should be” eligible for legal citizenship.
  •  We are 95% confident that between 60% and 66% of all registered voters nationwide will answer illegal immigrants “should be” eligible for legal citizenship.
  •  We are 95% confident that 63% of the 904 registered voters in the sample answered illegal immigrants “should be” eligible for legal citizenship.”
  •  We are confident that 95% of the 904 registered voters in the sample answered “should be.”

Question 2

Select one answer.

10 points

Living at home: According to a 2011 report from the U.S. Census, 59% of young men (age 18-24) are living at home with their parents.

Suppose that we plan to select a random sample of 100 young men from your community. If we use the national figure of 59%, we estimate that the standard error is about 0.05 for results from random samples of 100 young men from your community.

When we select a random sample of 100 young men from your community, we find that 50% are living at home. Which gives the best interpretation of the 95% confidence interval to estimate the percentage of young men in your community who are living at home?

  •  We are 95% confident that 50% of the young men in your community are living at home.
  •  We are 95% confident that 45% to 55% of the young men in your community are living at home.
  •  We are 95% confident that 40% to 60% of the young men in your community are living at home.

Question 3

Select one answer.

10 points

Academic advising: In 2014 the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. In a simulation we select random samples from this population. For each sample we calculate the proportion who rarely or never use academic advising services.

What is the smallest sample in the list below that will satisfy the conditions for the use of a normal model to represent the sampling distribution?

  •  15
  •  20
  •  25
  •  30

Question 4

Select one answer.

10 points

There are over 3 million students enrolled in community colleges in the U.S. A total of 443,818 students at 699 community colleges completed the Community College Survey of Student Engagement (CCSSE) between 2009 and 2011. About half (50%) of students reported that they “often” or “very often” prepare two or more drafts of a paper before turning it in.

True or false? The 50% is a statistic representing a sample of 443,818 community college students.

  •  True
  •  False

Question 5

Type numbers in the boxes.

Part 1: 10 points

Part 2: 10 points

20 points

Academic advising: In 2014, the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. In a simulation we select random samples from this population. For each sample we calculate the proportion who rarely or never use academic advising services.

If we repeatedly obtain random samples of 200 students, what will be the mean and standard deviation of the sampling distribution of sample proportions?

Mean (round to 2 decimal places AFTER completing all calculations):

Standard deviation (round to 3 decimal places AFTER completing all calculations):

Question 6

Select one answer.

10 points

Orange M&M’s: The M&M’s web site says that 20% of milk chocolate M&M’s are orange. Let’s assume this is true and set up a simulation to mimic buying 200 small bags of milk chocolate M&M’s. Each bag contains 55 candies. We made this dotplot of the results.

Now suppose that we buy a small bag of M&M’s. We find that 25.5% (14 of the 55) of the M&M’s are orange. What can we conclude?

  •  This result is not surprising because we expect to see many samples with 14 or more orange candies.
  •  This result is surprising because it is unlikely that we will select a random sample with 25.5% or more orange candies if 20% of milk chocolate M&M’s are orange.
  •  This result is surprising because we expect the orange candies to make up no more than 20% of the candies in a packet.

Question 7

Select one answer.

10 points

Orange M&M’s: The M&M’s web site says that 20% of milk chocolate M&M’s are orange. Let’s assume this is true and set up a simulation to mimic buying 200 small bags of milk chocolate M&M’s. Each bag contains 55 candies. We made this dotplot of the results.

The number of orange M&M’s was counted and here is a dotplot of the results:

Which of the following reasons best explains the variability we see in the proportion of orange M&M’s in the bags?

  •  Poor quality control in the production process
  •  Human error in calculating the proportion of orange M&M’s in a bag
  •  An error in the simulation
  •  The random selection of samples

Question 8

Select one answer.

10 points

Academic advising: In 2014, the Community College Survey of Student Engagement reported that 32% of the students surveyed rarely or never use academic advising services. Suppose that in reality, 42% of community college students rarely or never use academic advising services at their college. In a simulation we select random samples from this population. For each sample we calculate the proportion who rarely or never use academic advising services.

If we randomly sample 200 students from this population repeatedly, the standard error is approximately 3.5%. Is it unusual to see 32% who rarely or never use academic advising services in one of these samples?

  •  Yes, this is unusual because 32% is 2.9 standard errors below 42%. It is very rare for a sample to be nearly three standard errors from the mean.
  •  Yes, this is unusual because 32% is 10% lower than 42%.
  •  No, this is unusual because the error is only 10%.
  •  No, this is unusual because 32% is 2.9 standard errors below 42%.

Question 9

Select one answer.

10 points

STD study: A 2008 CDC study estimated that 26% of young women between the ages of 14 and 19 in the U.S. were infected with at least one of the most common sexually transmitted diseases (human papillomavirus [HPV]), chlamydia, herpes simplex virus, and trichomoniasis). Is the percentage lower in your community?

Suppose that we select a random sample of 100 young women in your community. We can use a normal model for the sampling distribution because the conditions are met. We expect 26 of the 100 to be infected with at least one of the most common STDs and 74 to not be infected. So we can find the Z-score and use the applet to assess the evidence provided by the data. (The standard error is about 0.044.) Here is a link to the applet.

Suppose that in a random sample of 100 young women in your community, 20% are infected with at least one of the most common STDs

True or false? We can conclude that the percentage of all young women in your community who are infected with at least one of the most common STDs is less than 26%.

  •  True
  •  False

Question 10

Select one answer.

10 points

Living at Home: According to a 2011 report from the U.S. Census, 59% of young men (age 18-24) are living at home with their parents. Is the percentage higher in your community?

Suppose that we select a random sample of 20 young men from your community. We cannot use a normal model for the sampling distribution because one of the conditions is not met since n(1–p) is not 10 or greater. We expect 41% of the young men are not living with their parents. This is 0.41(20) = 8.2. So we ran a simulation with p = 0.59 and n = 20.

Suppose that the sample of 20 young men from your community has 14 living at home. This is 70% of the sample.

Do the data suggest that the percentage of young men living at home in your community is higher than 59%?

  •  Yes, because 70% is an error of 11%.
  •  Yes, because it is unlikely that 70% or more will be living at home in a sample of 20 young men given the population percentage is 59%.
  •  No, because it is not surprising to see 70% or more living at home in a sample of 20 young men if 59% of all young men in the community live at home.
  •  No, because we expect results from random samples to vary. So 70% is not surprising.

 

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