OLI Module 8, Checkpoint 2 PDF

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OLI Module 8, Checkpoint 2 Sunday, October 27, 2019

17:55

1. Does secondhand smoke increase the risk of a low birthweight? A baby is considered have low birthweight if he/she weighs less than 5.5 pounds at birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birthweight. Suspecting that the national percentage is higher than 7.8%, researchers randomly select 1,200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy and find that 10.4% of the sampled babies are categorized as low birth weight. Let p be the proportion of all babies in the United States who are categorized as low birth weight. What are the appropriate null and alternative hypotheses for this research question?

H0:p=0.078 Ha:p>0.078 2. Does going to a private university increase the chance that a student will graduate with student loan debt? A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. A researcher wanted to see if there was a significant increase in the proportion of student loan debt for public and nonprofit colleges in 2014. Suppose that the researcher surveyed 1500 graduates of public and nonprofit universities and found that 71% of graduates had student loan debt in 2014. Let p be the proportion of all graduates of public nonprofit universities that graduated with student loan debt. What are the appropriate null and alternative hypotheses for this research question?

H0:p=0.69 Ha:p>0.69 3. A quality control engineer at a potato chip company tests the bag-filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 15% of bags are overfilled, then they stop production to fix the machine. They define overfilled to be more than 1 ounce above the weight on the package. The engineer weighs 100 bags and finds that 21 of them are overfilled. He plans to test the hypotheses: H 0 : p = 0.15 versus H a : p > 0.15 (where p is the true proportion of overfilled bags). What is the test statistic? Z=1.68

4. According to a Pew Research Center, in May 2011, 35% of all American adults had a smartphone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 300 community college students at random and finds that 120 of them have a smartphone. In testing the hypotheses H 0 , P = 0.35, versus H a , p > 0.35, she calculates the test statistic as Z = 1.82. Use the normal table to identify the appropriate p-value for this Z score. A. There is enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.034). B. There is enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.068). C. There is not enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.966). D. There is not enough evidence to show that more than 35% of community college students own a smartphone (p-value = 0.034).

A is correct!

5. A manufacturer of t-shirts marks a shirt as "irregular" when it has defects such as crooked seams, stains, rips, or holes. A small number of irregular t-shirts are expected as part of the manufacturing process, but if more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process. In order to test whether his plant is making a higher than expected number of irregular t-shirts, the manager of a plant randomly selects 100 t-shirts and finds that 12 are irregular. He plans to test the hypotheses: H 0 , P = 0.08, versus H a , p > 0.08 (where p is the true proportion of irregular t-shirts). What is the test statistic? Z=1.47

6. According to a 2015 survey by mobile loyalty company SessionM, 47% of smartphone users preferred nline shopping to in-store shopping. A professor at a local community college believes that the percentage of smartphone users who prefer online shopping may be higher among community college students. She randomly selects 150 community college students with smartphones and she finds that 84 of the students surveyed prefer online shopping. In testing the hypotheses: H 0 : p = 0.47 versus H a : p > 0.47, she calculates the test statistic as Z = 2.21. The alpha level for this problem is 0.05. Use the Normal Table to identify the appropriate p-value for this Z score. Given these results, which of the following is an appropriate conclusion? A. There is enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p-value = 0.0136). B. There is enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p-value = 0.0272). C. There is not enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p-value = 0.9864). D. There is not enough evidence to show that more than 47% of community college with smartphones prefer online shopping (p-value = 0.0136). A is correct!

7. The proportion of college football players who have had at least one concussion is estimated to be 34% in the United States. We wanted to know if football players at our university were less likely to have suffered a concussion, so we surveyed a random sample of 100 past and present football players at our university. Is this survey valid or not valid for testing the hypothesis that the proportion of college football players at our university with at least one concussion is less than the national average? A. Valid B. Not valid A. Valid

8. According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She decided to ask 100 architecture majors whether they had ever done an internship while at their university. She collected the responses and calculated that the proportion for her university was 43%. Which one of the following statements about the z-test is correct?

A. It is safe to use the z-test for p. B. It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one). C. It is not safe to use the z test for p, since n*p is not large enough. D. It is not safe to use the z-test for p, since n*(1−po) is not large enough. B. It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).

9. According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She decided to ask 100 architecture majors whether they had ever done an internship while at their university. She collected the responses and calculated that the proportion for her university was 43%. Which one of the following statements about the z-test is correct? A. It is safe to use the z-test for p. B. It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one). C. It is not safe to use the z test for p, since n*p is not large enough. D. It is not safe to use the z-test for p, since n*(1−po) is not large enough.

C. It is not safe to use the z test for p, since n*p is not large enough. 10. Suppose that a major polling organization wanted to test the hypothesis that there was a change in the president's "approval rating" since last month. Last month, 35% of the representative sample of registered voters approved of the president. For this month, the null hypothesis was that the approval rating equals 35% and the alternative hypothesis is that the approval rating does not equal 35%. The significance level for this test was 0.05. The results of the hypothesis test of the new survey showed a p-value of 0.008. Which of the following statements is correct? Check all that apply. A. The results were statistically significant. B. The results were not statistically significant. C. The null hypothesis should be rejected. D. The null hypothesis should be accepted. E. The null hypothesis cannot be rejected.

A. The results were statistically significant. C. The null hypothesis should be rejected. 11. A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. Dr. Blackman wanted to find out if her public nonprofit university had a lower proportion of students who graduated with student loan debt in 2013. For this survey, the null hypothesis was that the proportion of students with graduated with student loan debt equals 69% and the alternative hypothesis is that the proportion with student loan debt does not equal 69%. The significance level for this test was 0.05. The results of the hypothesis test of the new survey showed a p-value of 0.039. Which of the following statements is correct? Check all that apply. A. The results were statistically significant. B. The results were not statistically significant.

C. The null hypothesis should be rejected. D. The null hypothesis should be accepted. E. The null hypothesis cannot be rejected.

A. The results were statistically significant. C. The null hypothesis should be rejected. 12. According to Facebook's self-reported statistics, the average Facebook user has 130 Facebook friends. For a statistics project a student at Contra Costa College tests the hypothesis that CCC students will average more than 130 Facebook friends. She randomly selects 3 classes from the schedule of classes and distributes a survey in these classes. Her sample contains 45 students. Here are the null and alternative hypotheses for her study: H 0 : μ = 130, H a : μ > 130. What does μ represent in these hypotheses? A. Mean number of Facebook friends for the average user B. Mean number of Facebook friends for the CCC students in her sample. C. Mean number of Facebook friends for CCC students.

C. Mean number of Facebook friends for CCC students. 13. According to Facebook's self-reported statistics, the average Facebook user has 130 Facebook friends. For a statistics project, a student at Contra Costa College tests the hypothesis that CCC students will average more than 130 Facebook friends. She randomly selects 3 classes from the schedule of classes and distributes a survey in these classes. Her sample contains 45 students. Here are the null and alternative hypotheses for her study: H 0 : μ = 130, H a : μ > 130. From her survey data, the statistics student calculates that the mean number of Facebook friends for her sample is 138.7 with a standard deviation of 79.3. She analyzed her data using a t-test and obtained a P- value of 0.23. What conclusion can she draw from her data? A. Nothing. The conditions for use of a t-test were not met. She cannot trust that the P-value is accurate for this reason. B. Even though 138.7 is larger than 130, it is not significantly larger than 130. In other words, the data do not provide enough evidence to conclude that the mean number of Facebook friends of all CCC college students is higher than 130. C. The sample value of 138.7 is significantly larger than 130. In other words the data provide provide enough evidence to conclude that the mean number of Facebook friends of all CCC college students is higher than 130.

B. Even though 138.7 is larger than 130, it is not significantly larger than 130. In other words, the data do not provide enough evidence to conclude that the mean number of Facebook friends of all CCC college students is higher than 130. 14. According to Facebook's self-reported statistics, the average Facebook user is connected to 80 community pages, groups, and events. For a statistics project, a student at Contra Costa College tests the hypothesis that CCC students will average less than 80 such connections. She posts a survey on her Facebook page. Her sample contains 45 responses. She chooses a 5% level of significance. From her data she calculates a t-test statistic of approximately −1.74 with a P-value of about 0.04. What can she conclude? A. Nothing. The conditions for use of a t-test are not met. She cannot trust that the P-value is accurate

for this reason. B. The data is not statistically significant. In other words, the data do not provide enough evidence to conclude that the mean number of Facebook connections to community pages, groups and events of all CCC college students is less the 80. C. The data is statistically significant. In other words, the data do provide enough evidence to conclude that the mean number of Facebook connections to community pages, groups and events of all all CCC college students is less the 80.

A. Nothing. The conditions for use of a t-test are not met. She cannot trust that the Pvalue is accurate for this reason.

15. In 2013, the average Girl Scout in New York City sold 96 boxes of cookies. The leader of Troop 5078 in New York City wants to know if the scouts in her troop sold more cookies than the average in New York City. She randomly samples 50 girls in Troop 5078 and records the number of boxes of cookies sold for each girl in the sample. Here are the null and alternative hypotheses for her study: H 0 : μ = 96, H a : μ > 96. What does μ represent in these hypotheses? A. Mean number of boxes of cookies sold for the average Girl Scout in New York City B. Mean number of boxes of cookies sold for the Girl Scouts in her sample from Troop 5078 C. Mean number of boxes of cookies sold for the Girl Scouts in Troop 5078

C. Mean number of boxes of cookies sold for the Girl Scouts in Troop 5078

16. In 2013, the average Girl Scout in New York City sold 96 boxes of cookies. The leader of Troop 5078 in New York City wants to know if the scouts in her troop sold more cookies than the average in New York City. She randomly samples 50 girls in Troop 5078 and records the number of boxes of cookies sold for each girl in the sample. The troop leader finds that her Girl Scouts each sold an average of 101.1 boxes of cookies with a standard deviation of 29.3. She analyzed her data using a t-test and obtained a p-value of 0.11. What conclusion can she draw from her data? A. Nothing. The conditions for use of a t-test were not met. She cannot trust that the pvalue is accurate for this reason. B.Even though 101.1 is larger than 96, it is not significantly larger than 96. In other words, the data do not provide enough evidence to conclude that the mean number of boxes of cookies sold by Girl Scouts in Troop 5078 was higher than 96. C. The sample value of 101.1 is significantly larger than 96. In other words, the data provide enough evidence to conclude that the mean number of boxes of cookies sold by Girl Scouts in Troop 5078 was higher than 96. B. Even though 101.1 is larger than 96, it is not significantly larger than 96. In other words, the data do not provide enough evidence to conclude that the mean number of boxes of cookies sold by Girl Scouts in Troop 5078 was higher than 96. 17. A students in a statistics class needs to do a project and decides to find out if the average high school GPA of students in a statistics course at her university is higher than the average high

school GPA for their university. The university's average high school GPA of enrolled students in their year was 4.41. She emails a survey to all of her friends that are taking statistics and asks them what their high school GPA is. Her sample contains 18 responses. She chooses a 5% level of significance. From her data, she calculates a t-test statistic of approximately 1.41 with a p-value of about 0.08. What can she conclude? A. Nothing. The conditions for use of a t-test are not met. She cannot trust that the p-value is accurate for this reason. B. The data is not statistically significant. In other words, the data do not provide enough evidence to conclude that the mean GPA of students taking statistics at her university is higher than 4.41. C. The data is statistically significant. In other words, the data do provide enough evidence to conclude that the mean GPA of students taking statistics at her university is higher than 4.41.

A. Nothing. The conditions for use of a t-test are not met. She cannot trust that the pvalue is accurate for this reason. 18. The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour. When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. The FDA takes a random sample of 35 bags of flour for evaluation and finds that they contain an average of 80 insect parts per 100 grams, with a standard deviation of 6.3. Which hypothesis test should be used to determine whether the sample contains more than the allowed 75 insect parts per 100 grams? A. z-test for the population mean B. t-test for the population mean C. z-test for the population proportion D. t-test for the population proportion

B. t-test for the population mean 19. Water safety standards in southern California suggest that if a concentration of adenoviruses in the water is more than 1,000 per liter, further testing would have to be done to determine if the water was hazardous. A random sample of 45 water sources around San Diego showed an average of 1,023 adenoviruses per liter, with a standard deviation of 138.9. Which hypothesis test should be used to determine if the water samples contain more than the allowed 1,000 adenoviruses per liter? A. z-test for the population mean B. t-test for the population mean C. z-test for the population proportion D. t-test for the population proportion

B. t-test for the population mean 20. The dean of the engineering school at a technical university wants to emphasize the importance of having students who are gifted at reading and writing as well as math. She wants to know if she

can accurately claim that graduate students in engineering programs at her school have significantly higher scores on the verbal reasoning section of the GRE (a standardized test used in the admissions process for many graduate programs) than the national average for engineering students. The national average for the verbal reasoning GRE score for engineering students was 150 with a standard deviation of 9. A random sample of 49 engineering graduate students at her school were found to have an average verbal reasoning GRE score of 153. Which hypothesis test should be used to determine whether the engineering students at the dean's technical university have a higher verbal reasoning GRE score than the national average? A. z-test for the population mean B. t-test for the population mean C. z-test for the population proportion D. t-test for the population proportion

A. z-test for the population mean 21. The Wechsler Adult Intelligence Scale (IQ test) is constructed so that Full Scale IQ scores follow a normal distribution, with a mean of 100, and a standard deviation of 15. The mayor of Smart Town believes the county's residents are smarter than the national average and wants to use it (the intelligence of the residents) as a ...