Question 1

Testing hypotheses about differences in experimental treatments requires somemodifications to the procedures for testing hypotheses about differences in populationcharacteristics.
a) How are the hypotheses different?
b) How are the conditions different?
c) How are the conclusions different?

Accepted Answer

a) The hypotheses would have to be worded in terms of treatment means or proportions rather than population means or proportions. 
b) For experiments, the individuals or objects must be randomly assigned to treatments, whereas in testing hypotheses using data from sampling, the samples must be randomly selected. For experiments, the number of individuals in the treatment groups must be large or the distributions of the response variable would need to be approximately normal in very large treatment groups.For data from sampling, the assumption is that the samples are large or the population distributions are approximately normal. 
c) Conclusions would need to be worded in terms of treatment means or proportions. If random sampling from a population preceded the random assignment to treatments, it would be reasonable to generalize the conclusions about treatment effects to the population.

Question 2

The Internet is increasingly available to the general public, and this has not goneunnoticed by those who construct and give surveys. Researchers are using electronicsurveys more and more, which naturally leads to questions about the usefulness ofelectronic surveys compared to traditional mail and telephone surveys. One veryimportant aspect of surveys is the response rate. To study the difference in responserates between electronic and postal surveys, 377 college faculty members randomlyselected from a list of members in a single professional membership, the Mid-SouthEducational Research Association. Each person was assigned at random to eitherreceive the survey by the U. S. Postal Service (USPS) or by email. There were 189people in the USPS group and 188 people in the email group. Each group was sent afollow-up notice two weeks after the initial mailing. Each group was sent a follow-up notice two weeks after the initial mailing. Eighty-four of the USPS deliveredsurveys were returned, and 42 of the electronic surveys were returned.
(a) Construct and interpret a 95% confidence interval for the difference inproportions of surveys returned before being sent a follow-up notice for the mailand the email survey.
(b) In the context of this study, discuss the statistical significance and practicalsignificance of the results.
(c) To whom do you feel the results of this study can be generalized?
 Justify yourresponse in a few sentences.

Accepted Answer

a) Assumption check: Subjects were randomly assigned to treatment groups and there are at least 10 responses and at least 10 non-responses in each treatment groups.Thus, the large sample procedure (z) is appropriate.  
I am 95% confident that the difference in proportions of response between the USPS and email treatments is between 0.1285 and 0.3136.
 b) The confidence interval does not contain 0.It appears that the response rate is greater for the USPS.A difference in response rates that is between about 13 and 31 percentage points is large and would be of practical significance. 
c) It would be appropriate to generalize to the people in the professional organization, because the sample was a random sample from this population. However, the surveys were sent to college faculty in a single professional organization.College faculty are highly educated and probably use the Internet more than most; generalizing the results of this experiment beyond this group would not be appropriate.

Question 3

The Internet is increasingly available to the general public, and this has not goneunnoticed by those who construct and give surveys. Researchers are using electronicsurveys more and more, which naturally leads to questions about the usefulness ofelectronic surveys compared to traditional mail and telephone surveys. One veryimportant aspect of surveys is the response rate. To study the difference in responserates between electronic and postal surveys, 377 college faculty members randomlyselected from a list of members in a single professional membership, the Mid-SouthEducational Research Association. Each person was assigned at random to eitherreceive the survey by the U. S. Postal Service (USPS) or by email. There were 189people in the USPS group and 188 people in the email group. Each group was sent afollow-up notice two weeks after the initial mailing. Forty-eight of the USPSdelivered surveys were returned before the follow-up notice, and 24 of the electronicsurveys were returned before the follow-up notice.
(a) Construct and interpret a 95% confidence interval for the difference inproportions of surveys returned before being sent a follow-up notice for the mailand the email survey.
(b) In the context of this study, discuss the statistical significance and practicalsignificance of the results.
(c) To whom do you feel the results of this study can be generalized?
 Justify yourresponse in a few sentences.

Accepted Answer

a)  
b) The confidence interval does not contain 0.It appears that the response rate is greater for the USPS.A difference in response rates that is between about 5 and 20 percentage points is large and would be of practical significance. 
c) It would be appropriate to generalize to the people in the professional organization, because the sample was a random sample from this population. However, the surveys were sent to college faculty in a single professional organization.College faculty are highly educated and probably use the Internet more than most; generalizing the results of this experiment beyond this group would not be appropriate.

Question 4

Testing hypotheses about differences in experimental treatments requires somemodifications to the procedures for testing hypotheses about differences in populationcharacteristics.
a) How are the hypotheses different?
b) How are the conditions different?
c) How are the conclusions different?

Accepted Answer

The answer of Testing hypotheses about differences in experimental treatments...

Question 5

Proper nutrition is essential for aircraft pilots, given the demands of their job.Previous studies have indicated that United States Air Force pilots do not regularlyeat breakfast, and thus may have low blood glucose levels after fasting at night. Toinvestigate the potential for danger, 8 pilots were selected for study in flightsimulators. Each pilot participated in two trials and they tried a different drink, eitherDrink A (high carbohydrate) or Drink B (low carbohydrate) in each trial. The order inwhich the drinks were tried was determined at random. The second trial wasconducted 2 days after the first trial, so that any effects of the first drink wereeliminated. After consuming one of the drinks, the pilots were subjected to a varietyof attitude recovery tasks. (An attitude recovery task is one where the pilot mustreturn to wings-level flight.) The times to recovery are shown in the table below.Graphical displays of the data indicate that the t-procedure is appropriate.  Do these data provide convincing evidence that the mean attitude recovery timediffers for the two drinks?
 Provide appropriate statistical justification for yourconclusion.

Accepted Answer

The answer of Proper nutrition is essential for aircraft pilots,...

Question 6

Osteoarthritis of the knee is a degenerative disease causing joint pain, stiffness, anddecreased function. Usual treatment is a combination of physical therapy,medication, and arthroscopic surgery. The arthroscopic surgery involves removal ofcartilage fragments and calcium crystals, or the smoothing of bones to eliminatedifficulties with joint motion. Arthroscopic surgery is widely used, but it is not clearhow, or even if it works. In a recent study patients were randomly assigned to twotreatment groups. Patients in the arthroscopic surgery group received standardarthroscopic treatment plus physical therapy and medicine. Patients in the othergroup received only physical therapy and medicine. Two years after treatment thepatients were evaluated using standard scales for pain, stiffness, and physicalfunction. Higher scores indicate increased pain, increased stiffness, and decreasedphysical function. Physical function data from the study are summarized below.Graphical displays of the data indicate that it is reasonable to assume that the twophysical function score distributions are approximately normal.  
(a) What null hypothesis and alternative hypothesis might be used in this setting tocompare mean pain rating for the two treatments?
(b) For your hypotheses in part (a), what is the associated P-Value?
(c) Given your results in parts (a) and (b), what would you conclude about thedifference between the two treatments?
 Be sure to give your answer in the contextof this study.

Accepted Answer

The answer of Osteoarthritis of the knee is a degenerative...

Question 7

Osteoarthritis of the knee is a degenerative disease causing joint pain, stiffness, anddecreased function. Usual treatment is a combination of physical therapy,medication, and arthroscopic surgery. The arthroscopic surgery involves removal ofcartilage fragments and calcium crystals, or the smoothing of bones to eliminatedifficulties with joint motion. Arthroscopic surgery is widely used, but it is not clearhow, or even if it works. In a recent study patients were randomly assigned to twotreatment groups. Patients in the arthroscopic surgery group received standardarthroscopic treatment plus physical therapy and medicine. Patients in the othergroup received only physical therapy and medicine. Two years after treatment thepatients were evaluated using standard scales for pain, stiffness, and physicalfunction. Higher scores indicate increased pain, increased stiffness, and decreasedphysical function. Pain score data from the study are summarized below. Graphicaldisplays of the data indicate that it is reasonable to assume that the two pain scoredistributions are approximately normal. 
(a) What null hypothesis and alternative hypothesis might be used in this setting tocompare mean pain rating for the two treatments?
(b) For your hypotheses in part (a), what is the associated P-Value?
(c) Given your results in parts (a) and (b), what would you conclude about thedifference between the two treatments?
 Be sure to give your answer in the contextof this study.

Accepted Answer

The answer of Osteoarthritis of the knee is a degenerative...

Question 8

Proper nutrition is essential for aircraft pilots, given the demands of their job.Previous studies have indicated that United States Air Force pilots do notregularly eat breakfast, and thus may have low blood glucose levels after fastingat night. To investigate the potential for danger, 8 pilots were selected for studyin flight simulators. Each pilot participated in two trials and they tried a differentdrink, either Drink A (high carbohydrate) or Drink B (low carbohydrate) in eachtrial. The order in which the drinks were tried was determined at random. Thesecond trial was conducted 2 days after the first trial, so that any effects of thefirst drink were eliminated. After consuming one of the drinks, the pilots weresubjected to a variety of attitude recovery tasks. (An attitude recovery task is onewhere the pilot must return to wings-level flight.) The duration of self-illusorymotion (time between wings-level flight and the pilot to "feel" he or she hasreturned to wings-level flight) are shown in the table below. Graphical displaysof the data indicate that it is reasonable to assume that the two "felt recoverytime" distributions are approximately normal.  Do these data provide convincing evidence that the mean self-illusory motion timediffers for the two drinks?
 Provide appropriate statistical justification for yourconclusion.

Accepted Answer

The answer of Proper nutrition is essential for aircraft pilots,...

Exam 14: Learning From Experiment Data

Testing hypotheses about differences in experimental treatments requires somemodifications to the procedures for testing hypotheses about differences in populationcharacteristics. a) How are the hypotheses different? b) How are the conditions different? c) How are the conclusions different?

Testing hypotheses about differences in experimental treatments requires somemodifications to the procedures for testing hypotheses about differences in populationcharacteristics. a) How are the hypotheses different? b) How are the conditions different? c) How are the conclusions different?