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STAT 100 Lesson 12 Assignment
Answer the following questions and submit for grading. Each question or part of a question is worth 1 point.
1.
Researchers asked a sample of 50 1st grade teachers and a sample of 50 12th grade teachers how much of their own money they spent on school supplies in the previous school year. They wanted to see if teachers at one grade level spend more than teachers at the other grade level.
a.
What type of study is found—observational or randomized experiment? Explain.
b.
What is the experimental or observational unit?
c.
What is the response variable?
d.
What is the explanatory variable?
e.
Do we have to worry about confounding variables in this instance? Why? If so identify a possible confounding variable?
f.
Are either of the terms retrospective study or prospective study relevant? Explain.
2.
A research team compared two methods of measuring tread wear on tires. Eleven tires were each measured for tread wear by two different methods: one method was based on weight while the other method was based on groove wear. For convenience, each tire was measured first by weight method and then second by the groove wear.
a.
The two samples are which of the following: two independent or two dependent (matched pairs)? Explain.
b.
What type of study is found—observational or randomized experiment? Explain.
c.
What is the experimental or observational unit?
d.
What is the response variable?
e.
What is the explanatory variable?
3.
A study wants to determine if taking fish oils can reduce depressive symptoms. A group of 50 volunteers who suffered from mild depression were randomly divided into two groups. Each person was given a three-month’s supply of capsules. One group was given capsules that contained fish oils while the other group was given capsules that look and tasted like fish oils, but actually only contained sugar. Neither the participants nor the investigator knew what type of capsule they were taking. At the end of the month, a psychologist evaluated them to determine if their depressive symptoms had changed. Therefore, we are comparing the “change in depressive symptoms” for individuals in two groups. Explain whether each of the following terms applies to this study.
a.
observational study
b.
randomized experiment
c.
placebo
d.
placebo effect
e.
single-blind
f.
double-blind
g.
matched pairs (dependent samples)
h.
block design
i.
independent samples
j.
explanatory variable (What is it?)
k.
response variable (What is it?)
4.
Does the use of cell phones lead to a higher incidence of brain cancer? People with brain cancer were matched with people who did not have brain cancer on age, gender, and living environment. Each participant in the study was asked to answer questions about previous life experiences and exposures. Determine whether or not each of the following terms applies to this observational study.
a.
prospective
b.
retrospective
c.
case-control study
5.
A study involving ten people wants to compare the effectiveness of two different brands of antihistamines with regard to enhancing sleep. Each person is randomly assigned to take Antihistamine A on one night and Antihistamine B on the other night. With each person, the hours of sleep were recorded for each night. Explain whether each of the following terms applies to this study.
a.
observational study
b.
randomized experiment
c.
carry-over effect (confounding)
d.
matched pairs (dependent samples)
e.
explanatory variable (What is it?)
f.
response variable (What is it?)
6
.
Suppose the study found in the previous problem instead found that each person took Antihistamine A on the first night and Antihistamine B on the second night. What terms that did not apply to the previous problem now apply to this problem? Explain.
7.
Are you annoyed with spam e-mail? Suppose a random sample of 200 Penn State students was asked this question of which
8
0% said that they are annoyed. From the provided information we can find the following:
sample percent = 80% (sample proportion = .80)
standard deviation (S.D.) = .03
a.
Set up the calculation of a 95% confidence interval to estimate the population proportion of Penn State students who are annoyed by spam e-mail? (Hint: refer to Example 12.5)
b.
Knowing that the margin of error = .06 or 6%, write out a one-sentence interpretation of the margin of error.
c.
The 95% confidence interval to estimate the population proportion of Penn State students who are annoyed by spam e-mail is (.74 to .86). Write out a one-sentence interpretation of this confidence interval.
d.
What type of data is used in this example—categorical or measurement?
e.
What would happen to the size of the margin of error or confidence interval if the level of confidence were instead 99.7%? Explain.
8.
Explain what will happen to the width of a confidence interval (increase, decrease, or remain the same) as a result of each of the following changes:
a.
Population size is doubled from 5 million to 10 million
b.
Confidence level lowered from 98% to 90%
c.
Sample size is doubled from 500 to 1000
9.
A sample of 200 students in a Stat class were asked “How long did you sleep last night?” The results are found below.
sample mean = 6.4 hours
S.D. = 1.6 hours
standard error (S.E.) = .11 hours
sample size (n) = 200
a.
Set up the calculation of a 95% confidence interval to estimate the population mean number of hours slept last night.
b.
Knowing that the margin of error = .22, write out a one-sentence interpretation of the margin of error.
c.
The 95% confidence interval to estimate the population mean number of hours slept last night is (6.18 to 6.62) hours. Write out a one-sentence interpretation of this confidence interval.
d.
What type of data is used in this example?
e.
What would happen to the size of the margin of error or confidence interval if the level of confidence were instead 68%? Explain
10.
A 95% confidence interval for the proportion of women that have ever dozed off while driving is 0.07 to 0.
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. For men, a 95% confidence interval for the proportion that have ever dozed off while driving is 0.19 to 0.25. Assume both intervals were computed using large random samples.
a.
What conclusion can be made about the two population proportions that have dozed off while driving? Why?
b.
Rewrite each confidence interval in terms of percents rather than proportions. Does the conclusion remain the same? Explain.
c.
The two samples are which of the following: two independent or two dependent (matched pairs)?
d.
What type of data is found in this problem—categorical or measurement?
e.
Would the conclusion remain the same if the two confidence intervals had instead been calculated at 90% confidence? Explain.
11.
Attention Deficient Hyperactivity Disorder (ADHD) is a diagnosis applied to children who exhibit the following behaviors: (1) inattention (2) impulsiveness, (3) hyperactivity. ADHD is now known to be a lifelong problem where adolescents and adults continue to exhibit symptoms. Researchers at the University of Wisconsin (Heiligenstein E. et al., 1999) explored both psychological and academic functioning in ADHD college students. They reviewed charts of students who voluntarily sought a comprehensive assessment at the University’s Counseling and Consultation Services. Relevant charts were classified into two groups:
· Group 1 (ADHD group)
26
students who received a diagnosis of ADHD
· Control Group:
28
students who requested a career interest inventory but did not receive or request any counseling sessions beyond those needed for the career inventory
Students in both groups completed the Inventory of Common Problems (ICP). The ICP is an established self-report measure (inventory) of college student problems that includes 31 questions in seven subset areas. The two subset areas that we will examine are (1) Academic Problems and (2) Depression. In each subset area, there were four questions each where a rating of 1 to 5 was possible. Because of this, within each subset area, the minimum score was 4 points and the maximum score was 20 points.
a.
What type of observational study did the researchers at the University of Wisconsin use? Explain.
b.
The two samples are which of the following: two independent or two dependent (matched pairs)?
c.
Table 1 provides the results for the subset area: Academic Problems. What conclusion can be made when comparing the ADHD group to the control group? Why? Can you conclude that being ADHD causes a student to have a higher score in the subset area of academic problems? Explain.
Table A1.
Results for Subset Area: Academic Problems (Heiligenstein E. et al, 1999)
|
|
ADHD |
Controls |
|||
|
Sample Size (n) |
26 | 28 | |||
|
Mean Score |
14.5 points |
10.4 points |
|||
|
St Dev (S.D.) |
3.7 points |
3.9 points |
|||
|
S.E. |
.73 points |
.74 points |
|||
|
95% C.I. for Population Mean Subset Score |
14.5 ± 2(.73) = 14.5 ± 1.5 = approx (13 to 16 ) points |
10.4 ± 2(.74) = 10.4 ± 1.5 = approx (9 to 12) points |
d.
Table 2 provides the results for the subset area: Depression. What conclusion can be made when comparing the ADHD group to the control group? Why?
Table A2. Results for Subset Area: Depression (Heiligenstein E. et al, 1999)
|
8.3 points |
7.0 points |
|
|
2.5 points |
3.2 points |
|
| S.E |
.5 points |
.6 points |
|
8.3 ± 2(.5) = 8.3 ± 1.0 = approx (7 to 9) points |
7.0 ± 2(.6) = 7.0 ± 1.2 = approx (6 to 8) points |
12.
Are low carbohydrate diets effective? A random sample of six individuals who wanted to try a low carbohydrate diet was obtained. Each individual was placed on a low carbohydrate diet for eight weeks. The weight in pounds was determined for each individual both before and after the diet, as shown in Table A3.
a.
The two samples are which of the following: two independent or matched pairs? Explain.
b.
What type of study is found—observational or randomized experiment? Explain.
c.
What is the experimental or observational unit?
d.
What is the response variable?
e.
What is the explanatory variable?
f.
What sample(s) are used to calculate the appropriate confidence interval?
g.
The following information was obtained from the table found below.
sample mean difference = 13.2 pounds
S.D. = 13 pounds
standard error (S.E) = 5.2 pounds
sample size (n) = 6 people
Set up the calculation for a 95% confidence interval to estimate the population mean difference.
h.
Suppose the 95% confidence for the population mean difference in weight is (2.8 to 23.6) pounds. What conclusion can be made in this instance about the effectiveness of the diet? Explain in statistical terms.
i.
What is the advantage of using the differences rather than the original data in the calculation of the confidence intervals?
Table A3. Weight Before and After Diet
|
Person |
Weight Before Diet (pounds) |
Weight After Diet (pounds) |
Difference in pounds = (Before-After) |
|
|
1 |
125 |
1 17 |
8 | |
|
2 |
165 |
151 |
14 | |
|
3 |
205 |
169 |
36 |
|
|
4 |
115 |
-2 |
||
|
5 |
138 |
132 |
6 |
|
| 6 |
152 |
135 |
17 |
13.
Two methods of memorizing difficult material are being tested to determine if one method produces better retention. Nine pairs of students are included in the study. Each student in the pair has been matched according to IQ and academic background and then randomly assigned to use one of the two methods:
Method A
or
Method B
. A memorization test is given to all the students where the final score can range from 0 to 100 points.
Table A4. Memorization Methods
|
Sample |
95% C.I. for Population Mean Score on Memorization Test |
| Method A |
(50 to 74) points |
| Method B |
(45 to 73) points |
|
Difference = (Method A – Method B) |
(1 to 5) points |
a.
The two samples are which of the following: two independent or matched pairs? Explain.
b.
What type of study is found—observational or randomized experiment? Explain.
c.
What is the experimental or observational unit?
d.
What is the response variable?
e.
What is the explanatory variable?
f.
What confidence interval(s) from Table A4 should be used to compare the memorization score for the two methods? Explain.
g.
Using your answer in the previous part as your basis, state an appropriate conclusion in terms of the problem.
Please submit this assignment.
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Name________________________________
PSU ID_____________________________
STAT 100 Lesson 13 Assignment
Answer the following questions and submit for grading. Each question or part of a question is worth 1 point except: 1, 2A, 2B, 2C, 3E, 4E, 5D, &
6
C are worth 2 points; 7- 7 is worth 6 points.
1.
An ESP experiment is done in which a participant guesses which of 8 cards the researcher has randomly picked, where each card is equally likely to be selected. This is repeated for 200 trials. The null hypothesis is that the subject is guessing, while the alternative is that the subject has ESP and can guess at higher than the chance rate. Write out the type 1 and type 2 errors in terms of this problem.
2.
For each of the following, write out the null and alternative hypotheses. Also identify what type of data is found. Refer to the information in Table 13.1.
a.
Do female students, on the average, have a higher GPA?
b.
Is there a linear relationship between height and weight?
c.
Is there a difference in the proportions of male and female college students who smoke?
3.
A Researcher asked a sample of 50 1st grade teachers and a sample of 50 12th grade teachers how much of their own money they spent on school supplies in the previous school year. The researcher wanted to see if the mean spending at one grade level is different from the mean spending at another grade level.
Two-sample T for 1st_Grade vs 12th_Grade
N Mean StDev SE Mean
1st_Grade 50 111.2 88.9 13
12th_Grade 50 49.5 38.8 5.5
Difference = mu 1st_Grade – mu 12th_Grade
Estimate for difference: 61.7
95% CI for difference: (34.3, 89.1)
T-Test of difference = 0 (vs not =): T-Value = 4.50 P-Value = 0.000 DF = 66
Figure A.1.
a.
What is the response variable in this problem?
b.
What is the explanatory variable in this problem?
c.
What type of variable is the response variable? categorical or measurement
d.
What is the appropriate population value for this problem? population mean or population proportion
e.
Write out the null and alternative hypotheses in terms of the appropriate population value.
f.
On the output in Figure A.1 the test statistic is 4.50. Use this test statistic to write a one-sentence interpretation of the p-value in terms of this problem.
g.
What conclusion can be made in terms of this problem? Why?
h.
Using the 95% confidence interval of the difference as your basis, do you think practical significance has been found with regard to the mean amount spent when comparing 1st grade teachers to 12th grade teachers? Include reasoning. Hint: Refer to Example 13.10.
4.
A survey asked
2000
people whether or not they frequently exceed the speed limit. The collected data is summarized in the following contingency table. The goal is to determine if there is a difference in the population proportion that say “yes” when comparing those who are under 40 years in age to those who are at least 40 years in age.
Table A.1. Data Summary
|
Frequently Exceed the Speed Limit? |
||||
|
Age |
Yes |
No |
Total |
|
| Age under 40 |
600 (60%) |
400 |
1000 |
|
|
Age 40 and above |
450 (45%) |
550 |
||
|
1050 |
950 |
2000 |
a.
What is the response variable in this problem?
b.
What is the explanatory variable in this problem?
c.
What type of variable is the response variable? categorical or measurement
d.
What is the appropriate population value for this problem? population mean or population proportion
e.
Write out the null and alternative hypotheses in terms of the appropriate population value.
f.
On the output found in Figure A.2 the test statistic is 6.72. Use this test statistic to write out a one-sentence interpretation of the p-value in terms of this problem.
g.
What conclusion can be made in terms of this problem? Why?
h.
Compare the sample percent (proportion) that said yes for the two age groups that are found in Table A.1. Do you believe the results are practically significant? Include reasoning.
i.
Could a Chi-square Test also be used to analyze this data? Why? (Hint: Refer back to lesson assignments in Lesson 7.)
Test and CI for Two Proportions
Sample X N Sample p
< 40 yrs 600 1000 0.60
≥ 40 yrs 450 1000 0.45
Estimate for p(1) – p(2): 0.15
95% CI for p(1) – p(2): (0.107, 0.193)
Test for p(1) – p(2) = 0 (vs not = 0): Z = 6.72 P-Value = 0.000
Figure A.2.
5.
For patients with a particular disease, the population proportion of those successfully treated with a standard treatment that has been used for many years is .75. A medical research group invents a new treatment that they believe will be more successful, i.e., population proportion will exceed .75. A doctor plans a clinical trial he hopes will prove this claim. A sample of 100 patients with the disease is obtained. Each person is treated with the new treatment and eventually classified as having either been successfully or not successfully treated with the new treatment.
a.
What is the response variable in this problem?
b.
What type of variable is the response variable? categorical or measurement
c.
What is the appropriate population value for this problem? population mean or population proportion
d.
Write out the null and alternative hypotheses in terms of the appropriate population value.
e.
Find the test statistic on the output found below. Use this test statistic to write a one-sentence interpretation of the p-value in terms of this problem.
f.
What conclusion can be made in terms of this problem? Why?
Test and CI for One Proportion
Test of p = 0.75 vs p > 0.75
Sample X N Sample p Z-Value P-Value
1 80 100 0.800000 1.15 0.124
Figure A.3.
6. Refer to the information found in the article entitled 21st Birthday from the Penn State Pulse (January, 2001). This was previously used in Lesson 9.
a.
What is the majority of the type of data summarized on the first page of this article? Measurement or categorical
b.
What population value should be used with this data? population mean or population proportion
c.
At the bottom of the first page of the article you find the statement “* statistically significant at the .05 level.” This statement implies that the p-value is ≤ .05. Find the “*”s on the first page of the article. Precisely what two results are statistically significant? State these results in terms of the appropriate population value (ie: population mean or population proportion).
Source: Penn State Pulse, 21st Birthday, January 2001
7. Refer to the following article located in the Library Reserves–use the Library Reserves link in Angel
Source: Kirchheimer, S. (May 17, 2003). Secondhand Smoke Study Raises Ire
Answer the following questions about the article.
Question 1:
In studies that compare never smokers married to smokers with never smokers married to never smokers, the explanatory variable is ______
a.
whether or not the spouse smokes.
b.
whether or not the person was married.
c.
whether or not the person developed lung cancer.
d.
whether or not the smoke is secondhand.
Question 2:
A study that compares never smokers married to smokers with never smokers married to never smokers is which of the following?
a.
randomized experiment
b.
observational study
c.
matched pairs study
Question 3:
The number 30% in this article represents which of the following quantities?
a.
risk
b.
relative risk
c.
increased risk
d.
odds
Question 4:
Enstrom’s study is which of the following?
a.
randomized experiment
b.
prospective study
c.
retrospective study
Question 5:
This article identifies the funding source used by Enstrom. As a statistical sleuth, what should you conclude from Enstrom’s study after knowing his funding source?
a.
results are definitely biased
b.
must first evaluate scientific procedures used in study before interpreting results
c.
results are definitely unbiased
Question 6:
Which of the following is not a concern about the study that was conducted by Enstrom?
a.
extending conclusions to all people in the United States
b.
the existence of confounding variables
c.
smoking habits probably changed from 1972 to 1998
d.
results are based on a very small sample size
Question 7:
Now apply the seven critical components that are found in Chapter 2 of your textbook to this article. List out each component and provide a comment about each component based on what you have discovered when reading the article. If the article does not provide sufficient information about a certain component, just provide a plausible explanation and/or suggestion.
Please submit this assignment.
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