Answer The Following Questions And Submit For Grading

Answer The Following Questions And Submit For Grading Each Question O

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 88.0 12.5 12th Grade 50 49.5 38.8 5.5 Difference = mu 1st Grade - mu 12th Grade Estimate for difference: 61.7. CI for difference: (34.3, 89.1) T -Test of difference = 0 (vs not =): T -Value = 4.50 P -Value = 0.000 DF = 66. 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 (%) 40 and above (%) Total 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

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 ..15 0.124

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 “” 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 . 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.

Paper For Above instruction

The questions provided encompass a broad range of statistical concepts including hypothesis testing, data types, identifying response and explanatory variables, formulating hypotheses, interpreting p-values, and evaluating practical versus statistical significance. This paper will comprehensively address each of these questions within their respective contexts, applying statistical principles appropriately.

1. Errors in ESP hypothesis test

In the ESP experiment where a participant guesses among 8 cards across 200 trials, the null hypothesis states that the participant's guesses are purely by chance, with a probability of 1/8 (12.5%) for each trial, indicating no ESP ability. The alternative hypothesis suggests the participant has ESP, thus guessing at a rate higher than chance. A Type I error occurs if we incorrectly reject the null hypothesis when it is true—concluding the participant has ESP when they do not. Conversely, a Type II error involves failing to reject the null hypothesis when the alternative is true—failing to detect ESP when it genuinely exists.

2. Hypotheses and data types

a. To determine if female students have higher GPAs on average, the null hypothesis (H₀) states that the mean GPA of female students is equal to that of male students, while the alternative (H₁) states that the mean GPA of females is greater. This involves measurement data of GPA and a comparison of means.

b. For assessing a linear relationship between height and weight, H₀ asserts no correlation exists (correlation coefficient equals zero), and H₁ asserts that a correlation exists. The data involved are measurement variables, with hypotheses concerning correlation coefficients.

c. To evaluate if the proportions of male and female students who smoke differ, H₀ posits equal proportions, and H₁ suggests unequal proportions. The data are categorical, involving proportions of smoking.

3. Comparing school supply spending between grade levels

a. The response variable is the amount of money spent on school supplies, a measurement variable.

b. The explanatory variable is the grade level (1st versus 12th grade).

c. The response variable is measurement data.

d. The appropriate population value is the difference in mean spending between the two grade levels.

e. Null hypothesis: μ₁ − μ₂ = 0; Alternative hypothesis: μ₁ − μ₂ ≠ 0.

f. The test statistic of 4.50 indicates strong statistical evidence against the null hypothesis, suggesting a significant difference in mean spending.

g. The conclusion is that there is a statistically significant difference in mean expenditure on school supplies between 1st and 12th grade teachers, with 1st grade teachers spending more.

h. The 95% confidence interval (34.3 to 89.1) for the difference implies that the difference is not only statistically significant but also practically important, as the interval suggests a substantial mean difference in expenditure, reinforcing the practical significance.

4. Speeding behavior and age

a. The response variable is whether individuals frequently exceed the speed limit (categorical: yes/no).

b. The explanatory variable is age group (

c. The response variable is categorical.

d. The population value of interest is the proportion of individuals in each age group who frequently exceed the speed limit.

e. Null hypothesis: p₁ − p₂ = 0; Alternative hypothesis: p₁ − p₂ ≠ 0.

f. A test statistic of 6.72 implies very strong evidence against the null hypothesis, significant at the 0.05 level.

g. The conclusion is that significant differences exist in the proportions of speed limit exceeders between the two age groups.

h. The sample proportions suggest a practical difference, and if the confidence interval does not include zero, it confirms significance, which it does here.

i. Yes, a Chi-square test is appropriate for analyzing the independence of categorical variables in contingency tables.

5. Clinical trial for new treatment

a. The response variable is the treatment outcome: successful or not, a categorical variable.

b. The response variable is categorical.

c. The appropriate population parameter is the proportion of patients successfully treated.

d. Null hypothesis: p = 0.75; Alternative hypothesis: p > 0.75.

e. The test statistic, based on the sample proportion, indicates whether the observed success rate exceeds 75%.

Suppose the Z-value is given; if Z is large and P-value small, we reject H₀, concluding the new treatment is superior.

f. If the P-value is less than 0.05, we conclude that the new treatment's success rate exceeds 75%, supporting the alternative hypothesis.

6. Interpretation of the 21st birthday article

a. The majority of data summarized is categorical (e.g., responses categorized as yes/no, or drinking behavior).

b. The population proportion should be used, as data involve proportions of groups exhibiting certain behaviors.

c. The statistically significant results—marked by an asterisk—imply that these comparisons (e.g., proportion of students who engaged in risky behavior) differ significantly at the 0.05 level.

7. Critical evaluation of the smoking study

The explanatory variable is whether the spouse smokes (a). The study is observational (b), not experimental. The 30% figure represents risk (a). Enstrom’s study type is retrospective (c). Concerns include potential bias due to funding sources (a), confounding variables (b), behavioral changes over decades (c), and sample size limitations (d). The critical components—research question, sampling, measurement, analysis, conclusion, etc.—must be scrutinized to confirm validity and reliability, with particular emphasis on potential biases and confounding factors affecting the results.

References

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