Stat 3

Marijuana legalization: In a Public Policy Institute of California (PPIC) poll, 53% of 1,706 California adult residents surveyed say that marijuana should be legal. Based on the results, the 95% confidence interval is (0.506, 0.554). Which of the following is an appropriate interpretation of this confidence interval? http://blog.sfgate.com/smellthetruth/2015/03/25/majority-of-californians-ready-to-legalize-marijuana-new-poll-confirms/ A. We are 95% confident that between 50.6% and 55.4% of California residents say that marijuana should be legal. B. We can conclude that 95% of states have 50.6% to 55.4% of adult residents who say that marijuana should be legal. C. We are 95% confident that between 50.6% and 55.4% of all American adults say that marijuana should be legal. D. If we took many samples of adults from around the nation, between 50.6% and 55.4% of them would say that marijuana use should be legal.

A

The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The Central Limit Theorem says that A. the average burnout time of a large number of bulbs has a distribution that is close to Normal. B. the average burnout time of any number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. C. the average burnout time of any number of bulbs has a distribution that is close to Normal. D. the average burnout time of a large number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. E. as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type.

A

The number of hours a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The Central Limit Theorem says that the average burnout time of a large number of bulbs has a distribution that is close to Normal. the average burnout time of any number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. the average burnout time of any number of bulbs has a distribution that is close to Normal. the average burnout time of a large number of bulbs has a distribution of the same shape (strongly skewed) as the distribution for individual bulbs. as we look at more and more bulbs, their average burnout time gets ever closer to the mean for all bulbs of this type.

A

When the population is not normally distributed, the sampling distribution of the mean approximates which of the following? A. A distribution that is not normal B. A normal distribution given a large enough sample C. A slight positive skew D. A normal distribution

A

Which of the following is a reason that the marketing staff should not calculate a confidence interval for the proportion of all community residents who received the concert brochure by mail? Check all that apply. A. The sample needs to be random, but we don't know if it is. B. The actual count of community residents who received the concert brochure by mail is too small. C. The actual count of community residents who didn't receive the concert brochure by mail is too small. D. n^p is not greater than 10. E. n(1−^p) is not greater than 10.

A, B, & D

The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 119 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply. A. The sample needs to be random but we don't know if it is. B. The actual count of bike riders is too small. C. The actual count of those who do not ride a bike to campus is too small. D. n*^p is not greater than 10. E. n*(1−^p)is not greater than 10.

A, B, D

A doctor is measuring the mean systolic blood pressure of female students at a large college. Systolic blood pressure is known to have a skewed distribution. The doctor collects systolic blood pressure measurements from random sample of 28 female students. The resulting 90% confidence interval is (100.4, 159.6). Units of systolic blood pressure are mmHg. Which one of the following conclusions is valid? A. 90% of the female students at the college have a systolic blood pressure between 100.4 mmHg and 159.6 mmHg. B. The sampling distribution of means will probably not follow a normal distribution, so we cannot draw a conclusion. C. We are 90% confident that the mean systolic blood pressure for female students at the college is between 100.4 mmHg and 159.6 mmHg.

B

Confidence interval precision: We know that narrower confidence intervals give us a more precise estimate of the true population proportion. Which of the following could we do to produce higher precision in our estimates of the population proportion? A. We can select a lower confidence level and decrease the sample size. B. We can select a lower confidence level and increase the sample size. C. We can select a higher confidence level and decrease the sample size. D. We can select a higher confidence level and increase the sample size.

B

Suppose that the mean birth weight of human babies is 3135g. Hospital A records an average of 52 births a day. Hospital B records an average of 10 births a day. On a particular day, which hospital is less likely to record an average birth weight of 3435g or more? A. Hospital B (with 10 births a day), because with fewer births there will be less variability in mean birth weight. B. Hospital A (with 52 births a day), because the mean will typically be closer to 3135 g with more births. C. The two hospitals are equally likely to record such an event, because the birth weight of a baby does not depend on the number of babies born that day.

B

When the population is not normally distributed, the sampling distribution of the mean approximates which of the following? A distribution that is not normal B. A normal distribution given a large enough sample A slight positive skew A normal distribution

B

In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply. A. We take repeated random samples of size 10 from a population of unknown shape B. We take repeated random samples of size 15 from a population that is normally distributed. C. We take repeated random samples of size 50 from a population of unknown shape. D. We take repeated random samples of size 25 from a population that of unknown shape.

B & C

A researcher is estimating the mean income of residents in a large city. The income variable is usually skewed to the right. She collects a random sample of 25 people. The resulting 95% confidence interval is ($26700, $35400). Which one of the following conclusions is valid? A. We are 95% confident that the mean income for all residents of this city is between $26700 and $35400. B. 95% of the residents of this city have an income between $26700 and $35400. C. No conclusion can be drawn.

C

Consider random samples selected from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is 67 inches and the standard deviation is 3.8 inches. Which do you expect to have less variability (spread): a sampling distribution with sample size n = 112 or a sampling distribution with sample size n = 19? A. The sampling distribution with sample size n = 19 will have less variability. B. Both sampling distributions will have the same variability. C. The sampling distribution with sample size n = 112 will have less variability.

C

Genetically modified foods: In a Pew Research Center report from January 2015, 37% of American adults say that genetically modified (GM) foods are generally safe to eat. The margin of error for the 95% confidence interval is 3.1%. C. Funk and L. Raine. Public and Scientists' Views on Science and Society (2015) http://www.pewinternet.org/2015/01/29/chapter-3-attitudes-and-beliefs-on-science-and-technology-topics/#vaccines-and-access-to-experimental-treatments-18-point-gap What does this margin of error tell you about the results of the survey? A. We are 95% confident that the sample proportion is off by 3.1%. B. We are confident that 95% of the responses are within 3.1% of the population proportion. C. We are 95% confident that the population proportion is within 3.1% of the sample proportion of 37%. D. We are confident that population proportion is within 3.1% of the sample proportion of 37%.

C

In April and May of 2011, the Pew Research Center surveyed cell phone users about voice calls and text messaging. They found that 55% of those who send 51 or more text messages per day prefer to be contacted by text message rather than by a voice call. The margin of error for this sample was 5.7%. What does this margin of error tell you about the results of the survey? A. The results are off by 5.7%. B. 5.7% of the respondents gave a fake answer. C. The population proportion is most likely within 5.7% of the sample proportion from a randomly selected sample. D. We are sure that population proportion is within 5.7% of the sample proportion of 55%.

C

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? A. They apply to all students at the college. B. They apply only to the population of those who use the student parking lot. C. The results do not apply to any population because this was a convenience sample. D. They apply only to the population of those students who drive to the college.

C

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? A. There is a 95% probability that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%. B. We can be 95% confident that the proportion of the sample who use text messaging is between 73.1% and 76.9%. C. 95% of samples will have between 73.1% and 76.9% of respondents who use text messaging. D. We can be 95% confident that the proportion of all cell phone users who use text messaging is between 73.1% and 76.9%.

D

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. A larger sample size allows more people to give their input. B. A larger sample size means the sampling method isn't as important. C. A larger sample size gives a higher confidence level. D. A larger sample size gives a narrower confidence interval.

D

Race relations: A New York Times/CBS poll surveyed 1,027 adults nationwide about race relations in the United States. Of the sample, 61% responded that race relations in this country are generally bad. The 95% confidence interval is (0.58, 0.64). Which of the following is an appropriate interpretation of the 95% confidence interval? http://www.nytimes.com/2015/05/05/us/negative-view-of-us-race-relations-grows-poll-finds.html?_r=0 A. There is a 95% probability that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%. B. We are 95% confident that the proportion of the sample who say that race relations in this country are generally bad is between 58% and 64%. C. Of the samples, 95% will have between 58% and 64% of respondents who say that race relations in this country are generally bad. D. We are 95% confident that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.

D

A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate the average weight of the students at this university. The confidence interval was too wide to provide a precise estimate. True or false? The researcher could produce a narrower confidence interval by increasing the confidence level to 99%. True False

False

A researcher took a random sample of 100 students from a large university. She computed a 95% confidence interval to estimate the average weight of the students at this university. The confidence interval was too wide to provide a precise estimate. True or false? The researcher could produce a narrower confidence interval by increasing the sample size to 150. True False

True

Students in a statistics class conduct a survey to estimate the mean number of units students at their college are enrolled in. The students took a random sample of 50 students from their college. The students calculated a 90% confidence interval to estimate the mean number of units students at their college are enrolled in. The confidence interval was too wide to provide a precise estimate. The students are strategizing about how to produce a narrower confidence interval. True or false? The students could produce a narrower confidence interval by increasing the sample size to 100. True False

True

The bottle of Maria's favorite sports drink says that it holds 20 fluid ounces. Maria suspects that the sports drink actually holds a different amount. Maria takes a random sample of 25 bottles and measures the number of fluid ounces in each bottle. The mean fluid ounces of Maria's sample of 25 sports drinks is 21.5 fluid ounces. Assume that the standard deviation of fluid ounces for the entire population of sports drinks is 2 fluid ounces. True or false? Finding a random sample with a mean this high in a population with mean 20 fluid ounces and standard deviation 2 fluid ounces is very unlikely. True False

True