Chapter 5 Homework
A random sample of high school students were asked, "What is your favorite season?" Out of 468 students in Florida, 149 said winter, whereas only 76 out of 458 from New York said winter. We want to determine a 95% confidence interval for the difference in the proportions of students in the populations of Florida and New York who prefer winter. 95% confidence interval:
0.0982 to 0.2067 Florida (Group 1) n: 468 count: 149 New York (Group 2) n: 458 count 76
Student researchers at a private Midwestern college were interested in cell phone usage by students on campus and how it varied during different times of the day. They observed students walking around campus during the afternoon and recorded that 48 out of 232 students observed were using their phones in some fashion (so 184 were not). During the evening, they observed 45 out of 115 students using their phones (so 70 were not). We will assume these are representative samples from the population of all students at this college. Is the proportion of students on their phones during the afternoon different than in the evening? Calculate the difference in proportions (evening - day). Round answer to 3 decimal places, e.g. 0.298. Difference in proportions= ______
0.184 (45/115)-(48/232)
Researchers at Northwestern University explored whether meditation helps someone become a more compassionate person (Lim et al., 2015). To do this, they recruited 56 university students, all of whom reported little to no prior experience with meditation. The students were randomly assigned to one of two conditions: regularly completing a meditation session using the web-based application Headspace for three weeks or (as an active control group) completing a web-based cognitive training program from Lumosity for three weeks. To test the subjects on their level of compassion, they staged a scenario using three confederates. The subjects would enter a common waiting room, where there were three chairs. Two male confederates sat in two of the chairs, leaving one for the subject. After the subject was sitting for one minute, a female confederate came in, playing the role of a person suffering. She would walk in using crutches with some mild expressions of pain and then would lean against the wall with a sigh of discomfort. The sitting male confederates were trained to ignore her. What did the subjects do? It turned out that 10 of the 27 from the meditation group got up and offered the suffering woman their seat, while only 4 of the 29 in the active control group did so. Calculate the difference in proportions (mediation - control). Round answer to 3 decimal places, e.g. 0.295. Difference in proportions:
0.232 (10/27)-(4/29)
The General Social Survey is conducted every year and asks a variety of questions to a representative sample of non-institutionalized adults in the United States. In 2014, the survey showed that 45.6% of the 2,538 respondents said they were married. Forty years earlier, in 1974, the results showed that 77.8% of the 1,484 respondents said they were married. We want to calculate a 99% confidence interval for the difference in the proportions in the population that are married to compare the two time periods. Find the theory-based 99% confidence interval. Use order (1974 - 2014) and report answers as provided in the applet (no rounding).
0.2847 to 0.3601 Group 1 (2014) n: 2538 count: 1157 Group 2 (1974) n: 1484 count: 1155
A Pew Research study in April and May of 2013 asked single American adults whether they have ever broken up with someone by e-mail, text, or online message. Consider the following 2 × 2 table of counts: 1. What proportion of those 18-29 years old in the sample have broken up with someone by digital means. Round your answer to two decimal places e.g. 0.12. 2.. What proportion of those 30-64 years old in the sample have broken up with someone by digital means. Round your answer to two decimal places e.g. 0.12. 3. Would you say there is preliminary evidence of an association between age and breaking up with someone by digital means? a. Yes, since the conditional proportions are quite different. b. Yes, since the conditional proportions are very similar. c. No, since the conditional proportions are quite different. d. No, since the conditional proportions are very similar.
1. 0.22 2. 0.13 3. a/Yes, since the conditional proportions are quite different.
Student researchers at a private Midwestern college were interested in cell phone usage by students on campus and how it varied during different times of the day. They observed students walking around campus during the afternoon and recorded that 48 out of 232 students observed were using their phones in some fashion (so 184 were not). During the evening, they observed 45 out of 115 students using their phones (so 70 were not). We will assume these are representative samples from the population of all students at this college. Is the proportion of students on their phones during the afternoon different than in the evening? Use the Multiple Proportions applet to calculate and report the standardized statistic and p-value. Choose the answers that are closer to the values you obtained using the applet. Standardized statistic: ______ p-value: _____
3.61 and <0.001
Are there differences in the efficacy of duct tape versus cryotherapy in the treatment of the common wart? To answer this question, 61 participants between the ages of 3 to 22 years were randomly assigned to receive either traditional cryotherapy treatment or duct tape treatment for their wart. Of those enrolled, 51 completed the study. Use the Multiple Proportions applet to carry out a simulation-based test of significance and report the observed differences in proportions cured, the standardized statistic, and the p-value from the test. Choose the answers that are closer to the values you obtained using the applet. 1. Difference: standardized statistic: p-value: 2. Construct a 2SD approximate 95% confidence interval for the difference in the population proportions of warts cured between the two treatments. a. (-0.498, 0.006) b. (0.598, 1.094) c. (-0.370, -0.122) d. (0.352, 0.848)
Difference: 0.246 standardized statistic: -1.95 p-value: 0.06 2. a/(-0.498, 0.006)
Are metal bands used for tagging harmful to penguins? Researchers Saraux and colleagues (Nature, 2011) reported the results of a study done to investigate this using a sample of 100 penguins near Antarctica. These penguins had already been tagged with RFID chips, and the researchers randomly assigned 50 of them to receive a metal band on their flippers in addition to the RFID chip. The other 50 penguins did not receive a metal band. Researchers found that 16 of the banded penguins were still living 4.5 years into the study compared to 31 of the unbanded penguins that were still living. Are unbanded penguins more likely to be living after 4.5 years than are banded penguins? State the hypotheses either in words or using appropriate symbols. H0: Unbanded penguins are *just as /less/more/not* likely to be living after 4.5 years as banded penguins, πunbanded *><≠=* πbanded Ha: Unbanded penguins are *just as /less/more/not* as likely to be living after 4.5 years than banded penguins, πunbanded *><≠=* πbanded
Ho: just as likely = Ha: more likely >
Researchers at Northwestern University explored whether meditation helps someone become a more compassionate person (Lim et al., 2015). To do this, they recruited 56 university students, all of whom reported little to no prior experience with meditation. The students were randomly assigned to one of two conditions: regularly completing a meditation session using the web-based application Headspace for three weeks or (as an active control group) completing a web-based cognitive training program from Lumosity for three weeks. To test the subjects on their level of compassion, they staged a scenario using three confederates. The subjects would enter a common waiting room, where there were three chairs. Two male confederates sat in two of the chairs, leaving one for the subject. After the subject was sitting for one minute, a female confederate came in, playing the role of a person suffering. She would walk in using crutches with some mild expressions of pain and then would lean against the wall with a sigh of discomfort. The sitting male confederates were trained to ignore her. What did the subjects do? It turned out that 10 of the 27 from the meditation group got up and offered the suffering woman their seat, while only 4 of the 29 in the active control group did so. Use the Multiple Proportions applet to calculate and report the standardized statistic and p-value. Choose the answers that are closer to the values you obtained using the applet. Standardized statistic: p-value:
Standardized statistic: 1.98 p-value: 0.045
Are metal bands used for tagging harmful to penguins? Researchers Saraux and colleagues (Nature, 2011) reported the results of a study done to investigate this using a sample of 100 penguins near Antarctica. These penguins had already been tagged with RFID chips, and the researchers randomly assigned 50 of them to receive a metal band on their flippers in addition to the RFID chip. The other 50 penguins did not receive a metal band. Researchers found that 16 of the banded penguins were still living 4.5 years into the study compared to 31 of the unbanded penguins that were still living. Are unbanded penguins more likely to be living after 4.5 years than are banded penguins? Using a theory-based approach, determine the standardized statistic and corresponding p-value. Report answers as provided in the applet (no rounding). Put your numbers in the applet so you have a positive difference in proportions. Standardized statistic: p-value:
Standardized statistic: 3.01 p-value: 0.0013
Student researchers at a private Midwestern college were interested in cell phone usage by students on campus and how it varied during different times of the day. They observed students walking around campus during the afternoon and recorded that 48 out of 232 students observed were using their phones in some fashion (so 184 were not). During the evening, they observed 45 out of 115 students using their phones (so 70 were not). We will assume these are representative samples from the population of all students at this college. Is the proportion of students on their phones during the afternoon different than in the evening? Which of the following is a correct way to write out the hypotheses? a. H0: the proportion of students on their phones during the afternoon is the same as that in the evening; Ha: the proportion of students on their phones during the afternoon is different than in the evening b. H0: the proportion of students on their phones during the afternoon is the same as that in the evening; Ha: the proportion of students on their phones during the afternoon is greater than in the evening c. H0: the proportion of students on their phones during the afternoon is the same as that in the evening; Ha: the proportion of students on their phones during the afternoon is smaller than in the evening
a. H0: the proportion of students on their phones during the afternoon is the same as that in the evening; Ha: the proportion of students on their phones during the afternoon is different than in the evening
5.1.3 What value should you put in the cell with the question mark in the table so that there is no association between group and outcome? a. 60 b. 100 c. 70 d. 30 e. 35
a/60
Researchers at Northwestern University explored whether meditation helps someone become a more compassionate person (Lim et al., 2015). To do this, they recruited 56 university students, all of whom reported little to no prior experience with meditation. The students were randomly assigned to one of two conditions: regularly completing a meditation session using the web-based application Headspace for three weeks or (as an active control group) completing a web-based cognitive training program from Lumosity for three weeks. To test the subjects on their level of compassion, they staged a scenario using three confederates. The subjects would enter a common waiting room, where there were three chairs. Two male confederates sat in two of the chairs, leaving one for the subject. After the subject was sitting for one minute, a female confederate came in, playing the role of a person suffering. She would walk in using crutches with some mild expressions of pain and then would lean against the wall with a sigh of discomfort. The sitting male confederates were trained to ignore her. What did the subjects do? It turned out that 10 of the 27 from the meditation group got up and offered the suffering woman their seat, while only 4 of the 29 in the active control group did so. State the hypotheses using appropriate symbols. a. H0: πmediation = πnot; Ha: πmediation > πnot b. H0: p̂mediation = p̂not; Ha: p̂mediation < p̂not c. H0: p̂mediation = p̂not; Ha: p̂mediation > p̂not d. H0: πmediation = πnot; Ha: πmediation < πnot
a/H0: πmediation = πnot; Ha: πmediation > πnot
A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on telephone surveys. A national sample of 735 households was randomly selected, and all 735 of the households were sent an "advance letter" explaining that the household would be contacted shortly for a telephone survey. However, 368 households were randomly assigned to receive a monetary incentive along with the advance letter, and the other 367 households were assigned to receive only the advance letter. Here are the data on how many households responded to the telephone survey. Received an incentive and responded to survey: 286 total of receiving an incentive: 368 Did not receive an incentive and responded to survey: 245 total of not receiving an incentive: 367 What are the appropriate null and alternative hypotheses? a. Null: The proportion of all American households that would respond to the survey is the same whether offered a monetary incentive or not. Alternative: The proportion of all American households that would respond to the survey is greater when offered a monetary incentive than when not offered a monetary incentive. b. Null: The proportion of households in the sample that would respond to the survey is the same whether offered a monetary incentive or not. Alternative: The proportion of households in the sample that would respond to the survey is greater when offered a monetary incentive than when not offered a monetary incentive.
a/Null: The proportion of all American households that would respond to the survey is the same whether offered a monetary incentive or not. Alternative: The proportion of all American households that would respond to the survey is greater when offered a monetary incentive than when not offered a monetary incentive.
A survey of 122 statistics students included a question that asked them if they are a regular coffee drinker and if they took a nap in the past 3 days. Use the results shown in this mosaic plot to answer the questions. Were there more regular coffee drinkers than non-coffee drinkers in the results? a. Yes, there are more regular coffee drinkers than non-coffee drinkers in the sample because the width of the bar for coffee drinkers is wider than the width of the bar for non-coffee drinkers. b. There is not enough information to answer as we do not have the sample size from each group (regular coffee drinkers and non-coffee drinkers). c. Yes, there are more regular coffee drinkers who are nappers than non-coffee drinkers who are nappers in the sample because the height of the "nap" bar for regular coffee drinkers is higher than the height of the "nap" bar for non-coffee drinkers
a/Yes, there are more regular coffee drinkers than non-coffee drinkers in the sample because the width of the bar for coffee drinkers is wider than the width of the bar for non-coffee drinkers.
Suppose you are testing to see whether the proportion of males who voted in the last election differs from the proportion of females who voted in the last election. Which of these is NOT a correct way to write the null hypothesis? a. p̂M = p̂F b. πM = πF c. πM − πF = 0 d. The proportion of males in the population who voted in the last election is the same as the proportion of females in the population who voted in the last election.
a/p̂M = p̂F
The General Social Survey is conducted every year and asks a variety of questions to a representative sample of non-institutionalized adults in the United States. In 2014, the survey showed that 45.6% of the 2,538 respondents said they were married. Forty years earlier, in 1974, the results showed that 77.8% of the 1,484 respondents said they were married. We want to calculate a 99% confidence interval for the difference in the proportions in the population that are married to compare the two time periods. Describe the parameter we want to estimate and assign appropriate symbols to it. a. π1974 − π2014 = the difference in proportions of married people in the populations in 1974 and in 2014 b. p̂1974 − p̂2014 = the difference in proportions of married people in the samples in 1974 and in 2014
a/π1974 − π2014 = the difference in proportions of married people in the populations in 1974 and in 2014
Suppose you sample from two large populations and find sample proportions of p̂1 = 120/300 and p̂2 = 125/500. Suppose you are going to complete a test of significance using these proportions to see whether there is strong evidence that the population proportions differ. Which of the following is the correct value for the appropriate statistic? a. 0.325 b. 0.15 c. 0.25 d. 0.40
b/0.15 (120/300)-(125/500)
Are metal bands used for tagging harmful to penguins? Researchers Saraux and colleagues (Nature, 2011) reported the results of a study done to investigate this using a sample of 100 penguins near Antarctica. These penguins had already been tagged with RFID chips, and the researchers randomly assigned 50 of them to receive a metal band on their flippers in addition to the RFID chip. The other 50 penguins did not receive a metal band. Researchers found that 16 of the banded penguins were still living 4.5 years into the study compared to 31 of the unbanded penguins that were still living. Are unbanded penguins more likely to be living after 4.5 years than are banded penguins? Are the validity conditions met here for theory-based methods? Explain. a. No, because there are not at least 10 successes and at least 10 failures in each group, banded and unbanded. b. No, because the sample size in each group (banded and unbanded) are not the same. c. Yes, because there are at least 10 successes and at least 10 failures in each group, banded and unbanded. d. Yes, because the sample size in each group (banded and unbanded) is at least 20.
c/yes, because there are at least 10 successes and at least 10 failures in each group, banded and unbanded.
The General Social Survey is conducted every year and asks a variety of questions to a representative sample of non-institutionalized adults in the United States. In 2014, the survey showed that 45.6% of the 2,538 respondents said they were married. Forty years earlier, in 1974, the results showed that 77.8% of the 1,484 respondents said they were married. We want to calculate a 99% confidence interval for the difference in the proportions in the population that are married to compare the two time periods. Are the validity conditions met for this method? Explain. a. We need the sample size to be the same in both groups. These validity conditions are not met because there are 2,538 respondents in the 2014 group, and 1,484 respondents in the 1974 group. b. We need at least 10 successes and at least 10 failures in each group. These validity conditions are met because there are about 1,157 and 1,155 successes and 1,381 and 330 failures. c. We need each group to have a sample size of at least 20. These validity conditions are met because there are 2,538 respondents in the 2014 group, and 1,484 respondents in the 1974 group.
b/We need at least 10 successes and at least 10 failures in each group. These validity conditions are met because there are about 1,157 and 1,155 successes and 1,381 and 330 failures.
Suppose a 95% confidence interval for the difference in the proportion of female students who regularly drink coffee and the proportion of male students who regularly drink coffee (πF - πM) is (-0.023, 0.137). From this, can you can conclude that: a. You have strong evidence that the proportion of male students who regularly drink coffee is larger than the proportion of female students who regularly drink coffee. b. You do not have strong evidence that the proportion of male student who regularly drink coffee differs from the proportion of female students who regularly drink coffee. c. You have strong evidence that the proportion of male student who regularly drink coffee differs from the proportion of female students who regularly drink coffee. d. You have strong evidence that the proportion of female students who regularly drink coffee is larger than the proportion of male students who regularly drink coffee. e. You have convincing evidence that the proportion of male student who regularly drink coffee is the same as the proportion of female students who regularly drink coffee.
b/You do not have strong evidence that the proportion of male student who regularly drink coffee differs from the proportion of female students who regularly drink coffee.
Suppose that in a randomized experiment investigating the effect of incentive on whether a person agrees to take a survey, the data are as given in this table. What is an appropriate way to evaluate the effectiveness of the incentive? a. Compare 60/100 to 40/100 b. Compare 48/55 to 7/55 c. Compare 48/60 to 7/40 d. Compare 48/100 to 7/100
c/Compare 48/60 to 7/40 took survey with the incentive and divide that by the total incentives took the survey with no incentive and divide that by total no incentives
A random sample of high school students were asked, "What is your favorite season?" Out of 468 students in Florida, 149 said winter, whereas only 76 out of 458 from New York said winter. We want to determine a 95% confidence interval for the difference in the proportions of students in the populations of Florida and New York who prefer winter. 95% confidence interval: 0.0982 to 0.2067 Interpret the confidence interval you obtained in the context of the study. a. There is a 0.95 probability that the proportion of Florida students who like winter is larger than the proportion of New York students who like winter by an amount that's at least 0.098 and at most 0.207. b. We are 95% confident that the proportion of Florida students who like winter is at least 0.098 and the proportion of New York students who like winter is at most 0.207. c. We are 95% confident that the proportion of Florida students who like winter is larger than the proportion of New York students who like winter by an amount that's at least 0.098 and at most 0.207. d. There is a 0.95 probability that the proportion of Florida students who like winter is at least 0.098 and the proportion of New York students who like winter is at most 0.207.
c/We are 95% confident that the proportion of Florida students who like winter is larger than the proportion of New York students who like winter by an amount that's at least 0.098 and at most 0.207.
A random sample of high school students were asked, "What is your favorite season?" Out of 468 students in Florida, 149 said winter, whereas only 76 out of 458 from New York said winter. We want to determine a 95% confidence interval for the difference in the proportions of students in the populations of Florida and New York who prefer winter. Are the validity conditions met for a theory-based interval? Explain. a. We need the sample size to be the same in both groups. These validity conditions are not met because there are 468 students in the Florida group, and 458 students in the New York group. b. We need each group to have a sample size of at least 20. These validity conditions are met because there are 468 students in the Florida group, and 458 students in the New York group. c. We need at least 10 successes and at least 10 failures in each group. These validity conditions are met because there are 149 and 76 successes and 319 and 382 failures.
c/We need at least 10 successes and at least 10 failures in each group. These validity conditions are met because there are 149 and 76 successes and 319 and 382 failures.
A survey of 122 statistics students included a question that asked them if they are a regular coffee drinker and if they took a nap in the past 3 days. Use the results shown in this mosaic plot to answer the questions. Are there more people that have taken naps in the past 3 days than have not taken naps in the results? Choose the best among the following statements. a. There is not enough information to answer as we do not have the percentage of nappers for the overall sample, only for the groups (regular coffee drinkers and non-coffee drinkers). b. No, there are more nappers among regular coffee drinkers but less nappers among non-coffee drinkers. So on average there are the same number of nappers and non-nappers. c. Yes, there are more nappers than non-nappers in both the regular coffee group and the non-coffee group; the proportion of the bar that represents nappers is greater than 50%.
c/Yes, there are more nappers than non-nappers in both the regular coffee group and the non-coffee group; the proportion of the bar that represents nappers is greater than 50%.
Suppose you sample from two large populations and find sample proportions of p̂1 = 120/300 and p̂2 = 125/500. Suppose you are going to complete a test of significance using these proportions to see whether there is strong evidence that the population proportions differ. Which of the these are the appropriate hypotheses for this test? a. H0: π1 = π2 = 0.50; HA: π1 ≠ π2 ≠ 0.50 b. H0: p̂1 = p̂2 = 0.50; HA: p̂1 ≠ p̂2 ≠ 0.50 c. H0: p̂1 = p̂2; HA: p̂1 ≠ p̂2 d. H0: π1 = π2; HA: π1 ≠ π2
d/H0: π1 = π2; HA: π1 ≠ π2
The General Social Survey is conducted every year and asks a variety of questions to a representative sample of non-institutionalized adults in the United States. In 2014, the survey showed that 45.6% of the 2,538 respondents said they were married. Forty years earlier, in 1974, the results showed that 77.8% of the 1,484 respondents said they were married. We want to calculate a 99% confidence interval for the difference in the proportions in the population that are married to compare the two time periods. 99% confidence interval: 0.2847 to 0.3601 Interpret the confidence interval you obtained in the context of the study. a. There is a 0.99 chance that the proportion of the population that's married was higher in 1974 than in 2014 by an amount between 0.285 and 0.360. b. For 99% of the sample, the proportion that's married was higher in 1974 than in 2014 by an amount between 0.285 and 0.360. c. For 99% of the population, the proportion that's married was higher in 1974 than in 2014 by an amount between 0.285 and 0.360. d. We are 99% confident that the proportion of the population that's married was higher in 1974 than in 2014 by an amount between 0.285 and 0.360.
d/We are 99% confident that the proportion of the population that's married was higher in 1974 than in 2014 by an amount between 0.285 and 0.360.
A random sample of high school students were asked, "What is your favorite season?" Out of 468 students in Florida, 149 said winter, whereas only 76 out of 458 from New York said winter. We want to determine a 95% confidence interval for the difference in the proportions of students in the populations of Florida and New York who prefer winter. Describe the parameter we want to estimate and assign appropriate symbols to it. a. p̂Florida - p̂NewYork = the difference in proportions of students in the samples of Florida and New York who do not prefer winter b. πFlorida - πNewYork = the difference in proportions of students in the populations of Florida and New York who do not prefer winter c. p̂Florida - p̂NewYork = the difference in proportions of students in the samples of Florida and New York who prefer winter d. πFlorida - πNewYork = the difference in proportions of students in the populations of Florida and New York who prefer winter
d/πFlorida - πNewYork = the difference in proportions of students in the populations of Florida and New York who prefer winter
A survey of 122 statistics students included a question that asked them if they are a regular coffee drinker and if they took a nap in the past 3 days. Use the results shown in this mosaic plot to answer the questions. Is there a larger proportion of nappers among those that regularly drink coffee or don't regularly drink coffee? There is a *smaller or larger* proportion of nappers among those who regularly drink coffee, because the graph shows roughly *60% or 55%* nappers in the regular coffee group compared to roughly *55% or 60%* nappers in the non-coffee group.
larger, 60%, 55%
Are there differences in the efficacy of duct tape versus cryotherapy in the treatment of the common wart? To answer this question, 61 participants between the ages of 3 to 22 years were randomly assigned to receive either traditional cryotherapy treatment or duct tape treatment for their wart. Of those enrolled, 51 completed the study. State your conclusions in terms of strength of evidence against the null hypothesis and include statements about generalizing and cause and effect. Difference: -0.246 standardized statistic: -1.95 p-value: 0.06 2SD approximate 95% confidence interval for the difference in the population proportions of warts cured between the two treatments: (-0.498, 0.006) We have *strong/moderate* evidence that the population proportions of warts cured between the two treatments are *different/the same* and that the type of treatment *has an effect/does not have an effect* on cure because the study was a *observational study/randomized experiment* with *strong/moderately* significant results.
moderate different has an effect randomized experiment moderately
A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on telephone surveys. A national sample of 735 households was randomly selected, and all 735 of the households were sent an "advance letter" explaining that the household would be contacted shortly for a telephone survey. However, 368 households were randomly assigned to receive a monetary incentive along with the advance letter, and the other 367 households were assigned to receive only the advance letter. Here are the data on how many households responded to the telephone survey. standardized statistic: 3.32 p-value: 0.0005 Complete the statement about the conclusion: Because the standardized statistic is *less/more* than *2/0.05* and the p-value is *less/more* than *0.05/2*, we have *weak/strong* evidence that the proportion of all American households that would respond to the survey is *greater/the same* whether offered a monetary incentive than when not offered a monetary incentive
more than 2 less than 0.05 strong greater when
Are there differences in the efficacy of duct tape versus cryotherapy in the treatment of the common wart? To answer this question, 61 participants between the ages of 3 to 22 years were randomly assigned to receive either traditional cryotherapy treatment or duct tape treatment for their wart. Of those enrolled, 51 completed the study. State your hypotheses both in words and using correct symbols. H0: The probabilities of warts cured between the two treatments are *same/different* HA: The probabilities of warts cured between the two treatments are *same/different*
same, different
A team of researchers (Singer et al., 2000) used the Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on telephone surveys. A national sample of 735 households was randomly selected, and all 735 of the households were sent an "advance letter" explaining that the household would be contacted shortly for a telephone survey. However, 368 households were randomly assigned to receive a monetary incentive along with the advance letter, and the other 367 households were assigned to receive only the advance letter. Here are the data on how many households responded to the telephone survey. Received an incentive and responded to survey: 286 total of receiving an incentive: 368 Did not receive an incentive and responded to survey: 245 total of not receiving an incentive: 367 what is the standardized statistic? what is the p-value?
standardized statistic: 3.32 p-value: 0.0005 Use the theory based applet n: is the total count: is the number of successes p hat: already calculated
Researchers at Northwestern University explored whether meditation helps someone become a more compassionate person (Lim et al., 2015). To do this, they recruited 56 university students, all of whom reported little to no prior experience with meditation. The students were randomly assigned to one of two conditions: regularly completing a meditation session using the web-based application Headspace for three weeks or (as an active control group) completing a web-based cognitive training program from Lumosity for three weeks. To test the subjects on their level of compassion, they staged a scenario using three confederates. The subjects would enter a common waiting room, where there were three chairs. Two male confederates sat in two of the chairs, leaving one for the subject. After the subject was sitting for one minute, a female confederate came in, playing the role of a person suffering. She would walk in using crutches with some mild expressions of pain and then would lean against the wall with a sigh of discomfort. The sitting male confederates were trained to ignore her. What did the subjects do? It turned out that 10 of the 27 from the meditation group got up and offered the suffering woman their seat, while only 4 of the 29 in the active control group did so. State your conclusion (with appropriate justification based on your p-value) in the context of the research question. Be sure to address the issues of causation and generalizability as well Standardized statistic: 1.98 p-value: 0.045 We have *strong/weak* evidence that those practicing meditation will be *more/less* likely than those not practicing meditation to be compassionate, and that the type of practice *does not/has* an effect on whether or not person shows compassion because the study was a *observational study/randomized experiment* with *not significant/significant* results.
strong more likely has an effect randomized experiment significant
Student researchers at a private Midwestern college were interested in cell phone usage by students on campus and how it varied during different times of the day. They observed students walking around campus during the afternoon and recorded that 48 out of 232 students observed were using their phones in some fashion (so 184 were not). During the evening, they observed 45 out of 115 students using their phones (so 70 were not). We will assume these are representative samples from the population of all students at this college. Is the proportion of students on their phones during the afternoon different than in the evening? State your conclusion (with appropriate justification based on standardized statistic and on your p-value compared to the stated significance level) in the context of the research question. Be sure to also address the issues of causation and generalizability. Standardized statistic: 3.61 p-value: <0.001 *There is not/There is* very strong evidence (based on the *large/small* standardized statistic and the extremely *large/small* p-value) that the proportion of students on their phones during the afternoon is *different/larger than* in the evening. We should be able to generalize the results of this study to all students at this college. Because this is an observational study, confounding variables *could be affecting/are not affecting* the results of this study; therefore, we *can/cannot* determine that the time of day caused the difference.
there is large small different could be affecting cannot
Are metal bands used for tagging harmful to penguins? Researchers Saraux and colleagues (Nature, 2011) reported the results of a study done to investigate this using a sample of 100 penguins near Antarctica. These penguins had already been tagged with RFID chips, and the researchers randomly assigned 50 of them to receive a metal band on their flippers in addition to the RFID chip. The other 50 penguins did not receive a metal band. Researchers found that 16 of the banded penguins were still living 4.5 years into the study compared to 31 of the unbanded penguins that were still living. Are unbanded penguins more likely to be living after 4.5 years than are banded penguins? State your conclusion (with appropriate justification based on your p-value and stated significance level) in the context of the research question. Be sure to also address the issues of causation and generalizability. We have *weak/very strong/moderate* evidence that unbanded penguins are *more/less* likely to be living after 4.5 years than banded penguins. Because this is *observational study/randomized study*, we *can/cannot* determine that the bands caused the difference. We should be able to generalize to penguins in the *sample/all penguins/like those in the study* but should be cautious about generalizing further because this wasn't a random sample from some larger population.
very strong more likely randomized study can penguins like those in the study