Statistics 100
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, & 6C 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. Usethis 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 |
1000 |
|
Total |
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 thearticle 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 ofthe 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.
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