Stats

In survey conducted by Quinnipiac University from October 25-31, 2011, 47% of a sample of 2,294 registered voters approved of the job Barack Obama was doing as president. What is the 99% confidence interval for the proportion of all registered voters who approved of the job Barack Obama was doing as president?

(0.443, 0.497)

In September 2011, Gallup surveyed 1,004 American adults and asked them whether they blamed Barack Obama a great deal, a moderate amount, not much, or not at all for U.S. economic problems. The results showed that 53% of respondents blamed Barack Obama a great deal or a moderate amount. Calculate the 99% confidence interval for the proportion of all American adults who blame Barack Obama a great deal or a moderate amount for U.S. economic problems.

(0.489, 0.571)

Smoking habits: A group of statistics students conducted a survey about smoking habits on campus to determine the proportion of students who believe that smoking hookah (a water pipe) is less harmful than smoking cigarettes. Of the 50 students surveyed, 45 think that smoking hookah is less harmful than smoking cigarettes. Which of the following is a reason that this group of students should not calculate a confidence interval for the proportion of all students who believe that smoking hookah is less harmful than smoking cigarettes? Check all that apply.

-The sample needs to be random but we don't know if it is. -The actual count of students who do not believe that smoking hookah is less harmful than smoking cigarettes is too small. -n(1 minus p-hat) is less than 10.

Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. (Source: Wang, W., and Parker, K. (2014). Record Share of Americans Have Never Been Married. Pew Research Center.) If we repeatedly obtain random samples of 50 adults, what is the standard deviation of the sampling distribution of sample proportions? Enter your answer in decimal form rounded to two decimal places.

0.06

A researcher is trying to decide how many people to survey. Which of the following sample sizes will have the smallest margin of error?

1000

Blue M&M's: The M&M's website says that 24% of milk chocolate M&M's are blue. Suppose that we buy 5 small packets of milk chocolate M&M's. Each packet contains 55 candies. Which sequence is the most likely for the percent of blue M&M's in these 5 packets?

20%, 24%, 31%, 27%, 36%

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?

25

Suppose we take a survey and use the sample proportion to calculate a confidence interval. Which level of confidence gives the confidence interval with the largest margin of error? 90%, 95%, or 99%?

99%

In the months leading up to an election, news organizations conduct many surveys to help predict the results of the election. Often news organizations will increase the sample size in the last few weeks before the election. Which of the following is the primary reason they increase the sample size?

A larger sample size gives a narrower confidence interval.

For their statistics project, a group of students want to determine the proportion of LMC students who eat fast food frequently. They select a random sample of 50 students and find that 22 report eating fast food frequently (more than 3 times a week.) What is the count of success? 22 What is the count of failures? 28 Can the students use this data to calculate a 95% confidence interval? yes, normality conditions are met

Count of success=22 Count of failures=28 Yes, normality conditions are met

Obesity: The National Center for Health Statistics conducted the National Health Interview Survey (NHIS) for 27,787 U.S. civilian noninstitutionalized adults in January - September 2014. According to an early release report, an estimated 29.9% of U.S. adults aged 20 and over were obese. Obesity is defined as a body mass index (BMI) of 30 kg/m 2 or more. True or false? The 29.9% is a parameter representing a population of 27,787 adults.

False

SAT scores: According to the College Board website, 1,672,395 students from the class of 2014 took the SAT, a globally recognized college admissions test. The mean mathematics score was 513 with a standard deviation of 120. Source: SAT College Board 2014 College Bound Seniors Total Group Profile Report (2014). College Board. True or false? The mean mathematics score of 513 is a statistic, representing the mean score for the sample of 1,672,395 students.

False

Researchers conducted a study to determine whether the majority of community college students plan to vote in the next presidential election. They surveyed 650 randomly selected community college students and found that 55% of them plan to vote. Which of the following are the appropriate null and alternative hypotheses for this research question?

H 0 : p = 0.50 p = 0.50 p = 0.50 H a : p > 0.50 p > 0.50 p > 0.50

Tutoring Services: The Community College Survey of Student Engagement reports that 46% of the students surveyed rarely or never use peer or other tutoring resources. Suppose that in reality 40% of community college students never use tutoring services available at their college. In a simulation we select random samples from a population in which 40% do not use tutoring. For each sample we calculate the proportion who do not use tutoring. If we randomly sample 500 students at a time, what will be the mean and standard error of the sampling distribution of sample proportions?

Mean =0.40 Standard error=0.022

One population proportion test: Which of the following situations involves testing a claim about a single population proportion?

The National Institute of Mental Health estimates that in 2012, 6.9% of all U.S. adults had at least one major depressive episode in the past year. The university health center director believes that the figure for female college students is higher than this.

A school district claims that the normal attendance rate for their schools is 95%. An educational advocate believes that the true figure is lower. She chooses a school day in October and chooses 120 random students from the district. On that day, 87.5% of the students attended school. Can she conduct a hypothesis test to determine whether the proportion of students who attend school is lower than 0.95?

No, because even though (120)(0.95) is at least 10, (120)(0.05) is less than 10. This means the normal model is NOT a good fit for the sampling distribution.

Does the confidence interval indicate that a majority of all American adults blame Barack Obama a great deal or a moderate amount for U.S. economic problems?

No, because the interval extends below 0.5, meaning that it is reasonably possible that a minority of all American adults feel this way.

Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. If we randomly sample 100 adults from this population, would it be unusual to see a sample with 13% who had never been married?

No, this is not unusual because 13% is less than 2 standard deviations from 20%.

Tutoring Services: The Community College Survey of Student Engagement reports that 46% of the students surveyed rarely or never use peer or other tutoring resources. Suppose that in reality 40% of community college students never use tutoring services available at their college. In a simulation we select random samples from a population in which 40% do not use tutoring. For each sample we calculate the proportion who do not use tutoring. If we randomly sample 100 students from this population, the standard error is approximately 5%. Would it be unusual to see 46% who do not use tutoring in a random sample of 100 students?

No, this would not be unusual because 46% is only 1.2 standard errors from 40%.

On September 25, 2011 Michael Vick, the quarterback for the Philadelphia Eagles broke his non-throwing hand in a football game against the New York Giants. ESPN then posted a poll on their website. The poll asked viewers to predict which team would win the NFC East Division. The Eagles play in the NFC East Division. By 4:15 pm, 914 fans had voted. 25% of them thought the Eagles would still win the division. What can we conclude from a 95% confidence interval about the opinions of ESPN viewers?

Nothing because the sample was not randomly selected

What does the 99% confidence level in the previous problem tell us?

Of confidence intervals with this margin of error, 99% will contain the population proportion.

College students and STDs: A recent report estimated that 25% of all college students in the United States have a sexually transmitted disease (STD). Due to the demographics of the community, the director of the campus health center believes that the proportion of students who have a STD is higher at his college. He tests H 0 : p = 0.25 versus H a : p > 0.25 . The campus health center staff select a random sample of 150 students and determine that 43 have been diagnosed with a STD. Conduct a hypothesis test to address the director's hypothesis. Use a 5% significance level to make your decision. Use the applet (at the top of this Checkpoint) to determine the P‐value. Which of the following is an appropriate conclusion based on the results?

Of the students surveyed at his college, 29% have an STD, but this is not strong enough evidence to conclude that the proportion of students at his college who have a STD is higher than the report's estimate.

Birthdays of hockey players: In Malcolm Gladwell's book "Outliers" he shares the work of Canadian psychologist Roger Barnsley, who noticed that a disproportionately high percentage of elite ice-hockey players have birthdays between January and March. A group of statistics students would like to test if this is true for the Los Angeles Kings 2010-2015 rosters (22 out of 57). After debating whether this set of hockey players can be viewed as a random sample of hockey players, they decide to run a hypothesis test anyway to practice finding the P‐value. They test the hypotheses H 0 : p = 0.25 versus H a : p > 0.25 . They use a significance level of 0.05. Their calculated test statistic is 2.37. Using the applet (at the top of this Checkpoint), what is the P‐value?

P‐value = 0.009

Gender and College Students: According to the U.S. Department of Education, approximately 57% of students attending colleges in the U.S. are female. A statistics student is curious whether this is true at her college. She tests the hypotheses H 0 : p = 0.57 versus H a : p ≠ 0.57 . She plans to use a significance level of 0.05. She calculates her test statistic to be 1.42. Using the applet (at the top of this Checkpoint), what is the P‐value?

P‐value = 0.156

Delta Flights: According to the Bureau of Transportation Statistics, 77.4% of Delta Airline's flights arrived on time in 2010. The company is trying to improve on-time arrivals. They test the hypotheses H 0 : p = 0.774 versus H a : p > 0.774 . They calculate a P‐value of 0.03. Using a significance level of 0.05, which of the following is the best explanation for how to use the P‐value to reach a conclusion in this case?

Since the P‐value is less than the significance level, we reject the null hypothesis.

Statistics students surveyed 135 students at Tallahassee Community College. From their data we are 95% confident that between 44.7% and 61.9% of all TCC students are female. The students realize that this interval contains a large margin of error. What can they do to make a narrower interval?

Survey more students

We survey a random sample of American River College students and ask if they drink coffee on a regular basis. The 90% confidence interval for the proportion of all American River College students who drink coffee on a regular basis is (0.262, 0.438). What will be true about the 95% confidence interval for these data?

The 95% confidence interval is wider than the 90% confidence interval.

Birthdays of hockey players: In Malcolm Gladwell's book Outliers, he shares the work of Canadian psychologist Roger Barnsley, who noticed that a disproportionately high percentage of elite ice-hockey players have birthdays between January and March. A group of statistics students would like to test if this is true for the Los Angeles Kings 2010-2015 rosters (22 out of 57 ). After debating whether this set of hockey players can be viewed as a random sample of hockey players, they decide to run a hypothesis test anyway to practice finding the P‐value. They test the hypotheses H 0 : p = 0.25 versus H a : p > 0.25 . The P‐value is small enough to reject the null hypothesis. Which of the following is an appropriate conclusion (if we assume the sample is random)?

The data provides strong evidence to conclude that the proportion of LA Kings hockey players who have birthdays between January and March is greater than 0.25.

Student loans: In an article from September 13, 2010, titled "Student Loan Default Rates Increase," the website ed.gov analyzes trends in default rates for student loans over time. For the year 2008, the default rate for graduates was 7%. This means that 7% of the students who graduated in 2008 and had student loans did not make payments to repay those loans. Suppose we select 3 random samples of 1000 students each from this population of graduates from 2008. Which of the following is most likely to occur with the three samples?

The number who have defaulted will vary in each sample due to the random selection of graduates.

Smartphone use: In a Pew Research report titled, "U.S. Smartphone Use in 2015" the author states that 48% of smartphone-dependent Americans had to cancel or shut off their cell phone service for a period of time because the cost of maintaining that service was a financial hardship. "Smartphone dependent" is defined as owning a smartphone, but lacking any other type of high-speed access at home and having limited options for going online other than their cell phone. Let's assume this is true and set up a simulation to randomly sample 50 adults from this population. For each sample, we calculate the proportion of smartphone-dependent adults who had to cancel or shut off their cell phone service. We'll repeat this process 1,000 times. The dotplot of the resulting 1,000 proportion calculations is displayed below. Which of the following reasons best explains the variability we see in the proportion of smartphone-dependent adults who have had to cancel or shut off their cell phone service in each sample?

The random selection of samples

Parking survey: For a class assignment, a group of statistics students set up a table near the student parking lot. They asked students who passed by to complete a quick survey about whether they support the building of a multi-level parking structure that would add 425 new spaces at the college. They used the information from the survey to calculate the 95% confidence interval: (0.53, 0.72). To which population does the confidence interval apply?

The results do not apply to any population because this was a convenience sample.

An interactive poll on the front page of the CNN website in October 2011 asked if readers would consider voting for Herman Cain, a Republican presidential candidate. A statistics student used the information from the poll to calculate the 95% confidence interval. He got (0.53, 0.59). He also conducted a hypothesis test. He found very strong evidence that more than half of voters would consider voting for Herman Cain. To what population do these conclusions apply?

The results do not apply to any population because this was a voluntary response sample.

Police body cameras: A survey of New York State residents asked about police officers having to wear video cameras on duty. The question stated, "Do you agree or disagree that police officers should carry video cameras for the purposes of filming their activities while on duty?" Most (88%) respondents agreed with this statement. Do Californians share the same opinion? A California-based civil rights group conducted a similar survey by randomly selecting 500 California residents, and 425 agreed that police officers should carry video cameras for the purposes of filming their activities while on duty. Conduct a hypothesis test to determine if the proportion of California residents who agree is different from New York residents. Use a 5% significance level to make your decision. Use the applet (at the top of this Checkpoint) to determine the P‐value. Which of the following is an appropriate conclusion based on the results?

The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.

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.

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 40% to 60% of the young men in your community are living at home.

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 60% and 66% of all registered voters nationwide will answer illegal immigrants "should be" eligible for legal citizenship.

Sexual assault in college: In a Washington Post/Kaiser Family Foundation poll conducted from January through March 2015, 46% of adults (ages 17‐26) who attended college during the past 4 years say it's unclear whether sexual activity when both people have not given explicit agreement is sexual assault. The survey methodology section states that the margin of error is ± 3.5% at the 95% confidence level. What does this margin of error tell you about the results of this poll?

We are 95% confident that the population proportion is within 3.5% of the sample proportion of 46%.

In a survey conducted by the Pew Research Center in 2010 41% of Americans support the legalization of marijuana in the U.S. The researchers note that the margin of error is ± 3% using 95% confidence. What does this margin of error tell you about the results of the survey?

We can be 95% confident that the proportion of all Americans who support legalization of marijuana is within 3% of 41%.

In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They surveyed a random sample of 1914 cell phone users. 75% of the sample use text messaging. The 95% confidence interval is (73.1%, 76.9%). Which of the following is an appropriate interpretation of the 95% confidence interval?

We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

In a study of the nicotine patch, 21% of those who used the patch for 2 months reported no smoking incidents in the following year. The 95% confidence interval is (17.4%, 24.8%). Which of the following is an appropriate interpretation of the 95% confidence interval?

We can be 95% confident that the proportion of all nicotine patch users who would report no smoking incidents in the following year is between 17.4% and 24.8%.

Community college students survey students at their college and ask, "Have you met with a counselor to develop an educational plan?" Of the 25 randomly selected students, 17 have met with a counselor to develop an educational plan. What is the 90% confidence interval for the proportion of all students at the college that have met with a counselor to develop an educational plan? (Answers may vary slightly due to rounding. Round SE to 2 decimal places before calcluating the margin of error.)

We should not calculate the 90% confidence interval because normality conditions are not met.

Texting while driving: The accident rate for students who didn't text while using a driving simulator was 7%. In a driver distraction study of 1,876 randomly selected students, the accident rate for students who texted while driving was higher than 7%. This difference was statistically significant at the 0.05 level. Which of the following best describes how we should interpret these results?

With a large sample, statistically significant results may actually be only a small improvement over the control group (depending on the size of the increase in percentages).

In a study of a new treatment for cold sores, researchers randomly assigned 2209 patients to use of the new topical medication or a placebo in a double-blind experiment. Cold sores healed more quickly with the new medication and the improvement was statistically significant at the 0.01 level. Results were published the Journal of the American Medical Association in 1997. Which of the following is an appropriate conclusion?

With a large sample, statistically significant results may come from a small improvement over the placebo.

Research in March 2019 suggests that 40% of U.S. adults approve of way President Trump is running the country. We randomly sample 50 U.S. adults and find that 35% approve of way President Trump is running the country. What is the probability that a random sample of 50 U.S. adults has less than 35% with this opinion?

about .24

Research suggests that about 60% of CSU graduates started at a community college. In random samples of 100 CSU graduates, the percentage who started at a community college varies. What is the probability that in a random sample of 100 CSU graduates the error is within 5% of the population proportion of 60%? In the calculation of standard error, round to two decimal places before calculating Z.In the calculation of Z, round to two decimal places before using the Normal Distribution Calculator.

about 68%

Gun rights vs. gun control: In a December 2014 report, "For the first time in more than two decades of Pew Research Center surveys, there is more support for gun rights than gun control." According to a Pew Research survey, 52% of Americans say that protecting gun rights is more important than controlling gun ownership. Gun rights advocates in a conservative city believe that the percentage is higher among city residents. They survey 200 city residents and find that 130 say that protecting gun rights is more important than controlling gun ownership. What is the test statistic?

z=3.68