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Stat 200 week 6 homework problems9.1.2 many high school student
- 1. STAT 200 Week 6 Homework Problems 9.1.2 Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology exam 84,199 of them were female. In that same year,of the 211,693 students who took the calculus AB exam 102,598 of them were female ("AP exam scores," 2013). Estimate the difference in the proportion of female students taking the biology exam and female students taking the calculus AB exam using a 90% confidence level. 9.1.5 Are there more children diagnosed with Autism Spectrum Disorder (ASD) in states that have larger urban areas over states that are mostly rural? In the state of Pennsylvania, a fairly urban state, there are 245 eight yearolds diagnosed with ASD out of 18,440 eight year olds evaluated. In the state of Utah, a fairly rural state, there are 45 eight yearolds diagnosed with ASD out of 2,123 eight year olds evaluated ("Autism and developmental," 2008). Is there enough evidence to show that the proportion of children diagnosed with ASD in Pennsylvania is more than the proportion in Utah? Test at the 1% level. 9.2.3 All Fresh Seafood is a wholesale fish company based on the east coast of the U.S. Catalina Offshore Products is a wholesale fish company based on the west coast of the U.S. Table #9.2.5 contains prices from both companies for specific fish types ("Seafood online," 2013)("Buy sushi grade," 2013). Do the data provide enough evidence to show that a west coast fish wholesaler is more expensive than an east coast wholesaler? Test at the 5% level. Table #9.2.5: Wholesale Prices of Fish in Dollars Fish
- 2. All Fresh Seafood Prices Catalina Offshore Products Prices Cod 19.99 17.99 Tilapi 6.00 13.99 Farmed Salmon 19.99 22.99 Organic Salmon 24.99 24.99 Grouper Fillet 29.99 19.99 Tuna 28.99 31.99 Swordfish 23.99 23.99 Sea Bass 32.99 23.99 Striped Bass 29.99 14.99 9.2.6 The British Department of Transportation studied to see if people avoid driving on Friday the 13th. They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate
- 3. the mean difference in traffic count between the 6th and the 13th using a 90% level. Table #9.2.6: Traffic Count Dates 6th 13th 1990, July 139246 138548 1990, July 134012 132908 1991, September 137055 136018 1991, September 133732 131843 1991, December 123552 121641 1991, December 121139 118723 1992, March 128293 125532 1992, March 124631 120249 1992, November 124609 122770 1992, November 117584 117263
- 4. 9.3.1 The income of males in each state of the United States, including the District of Columbia and Puerto Rico, are given in table #9.3.3, and the income of females is given in table #9.3.4 ("Median income of," 2013). Is there enough evidence to show that the mean income of males is more than of females? Test at the 1% level. Table #9.3.3: Data of Income for Males $42,951 $52,379 $42,544 $37,488 $49,281 $50,987 $60,705 $50,411 $66,760 $40,951 $43,902 $45,494 $41,528 $50,746 $45,183 $43,624 $43,993 $41,612 $46,313 $43,944 $56,708 $60,264 $50,053 $50,580 $40,202 $43,146
- 5. $41,635 $42,182 $41,803 $53,033 $60,568 $41,037 $50,388 $41,950 $44,660 $46,176 $41,420 $45,976 $47,956 $22,529 $48,842 $41,464 $40,285 $41,309 $43,160 $47,573 $44,057 $52,805 $53,046 $42,125 $46,214 $51,630 Table #9.3.4: Data of Income for Females $31,862 $40,550 $36,048 $30,752
- 7. $41,412 $31,330 $31,329 $33,184 $35,301 $32,843 $38,177 $40,969 $40,993 $29,688 $35,890 $34,381 9.3.3 A study was conducted that measured the total brain volume (TBV) (in ) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients ("SOCR data oct2009," 2013). Is there enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal? Test at the 10% level. Table #9.3.5: Total Brain Volume (in ) of Normal Patients 1663407 1583940 1299470
- 8. 1535137 1431890 1578698 1453510 1650348 1288971 1366346 1326402 1503005 1474790 1317156 1441045 1463498 1650207 1523045 1441636 1432033 1420416 1480171 1360810 1410213 1574808 1502702 1203344 1319737 1688990 1292641 1512571 1635918 Table #9.3.6: Total Brain Volume (in ) of Schizophrenia
- 10. 9.3.4 A study was conducted that measured the total brain volume (TBV) (in ) of patients that had schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal patients and table #9.3.6 contains the TBV of schizophrenia patients ("SOCR data oct2009," 2013). Compute a 90% confidence interval for the difference in TBV of normal patients and patients with Schizophrenia. 9.3.8 The number of cell phones per 100 residents in countries in Europe is given in table #9.3.9 for the year 2010. The number of cell phones per 100 residents in countries of the Americas is given in table #9.3.10 also for the year 2010 ("Population reference bureau," 2013). Find the 98% confidence interval for the different in mean number of cell phones per 100 residents in Europe and the Americas. Table #9.3.9: Number of Cell Phones per 100 Residents in Europe 100 76 100 130 75 84 112 84 138
- 12. 112 118 118 54 23 121 126 47 Table #9.3.10: Number of Cell Phones per 100 Residents in the Americas 158 117 106 159 53 50 78 66 88 92 42 3 150 72 86 113 50 58 70 109 37 32 85 101
- 13. 75 69 55 115 95 73 86 157 100 119 81 113 87 105 96 11.3.2 Levi-Strauss Co manufactures clothing. The quality control department measures weekly values of different suppliers for the percentage difference of waste between the layout on the computer and the actual waste when the clothing is made (called run-up). The data is in table #11.3.3, and there are some negative values because sometimes the supplier is able to layout the pattern better than the computer ("Waste run up," 2013). Do the data show that there is a difference between some of the suppliers? Test at the 1% level. Table #11.3.3: Run-ups for Different Plants Making Levi Strauss Clothing Plant 1 Plant 2 Plant 3 Plant 4
- 16. 4.3 3.4 5.2 2.8 19.7 -0.8 7.3 13 3 -3.9 7.1 42.7 7.6 0.9 3.4 1.4 70.2 1.5 0.7 3 8.5 2.4 6 1.3 2.9
- 17. 11.3.4 A study was undertaken to see how accurate food labeling for calories on food that is considered reduced calorie. The group measured the amount of calories for each item of food and then found the percent difference between measured and labeled food, . The group also looked at food that was nationally advertised, regionally distributed, or locally prepared. The data is in table #11.3.5 ("Calories datafile," 2013). Do the data indicate that at least two of the mean percent differences between the three groups are different? Test at the 10% level. Table #11.3.5: Percent Differences Between Measured and Labeled Food National Advertised Regionally Distributed Locally Prepared 2 41 15 -28 46 60 -6 2 250 8 25 145 6
- 19. -0.5 -10 6 measured− labeled( ) labeled *100% measured-labeled ( ) labeled *100% mm3 mm 3 STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup - Instructions Page 1 of 4
- 20. STAT200 Introduction to Statistics Assignment #3: Inferential Statistics Analysis and Writeup Assignment #3: Inferential Statistics Analysis and Writeup Purpose: The purpose of this assignment is to develop and carry out an inferential statistics analysis plan and write up the findings. There are two main parts to this assignment: ● Part A: Inferential Statistics Data Plan and Analysis ● Part B: Write up of Results Step 1: Prepare Data Plan, Analyze Data, and Complete Part A of the Assignment #3 Template ➢ Task 1: Select Variables. Review the variables you used for assignments #1 and #2. Select your qualitative socioeconomic variable as your grouping variable and the two expenditure variables from the variables used in these previous assignments. Fill in Table 1: Variables Selected for Analysis with name, description, and type of variable (i.e., qualitative or quantitative). ➢ Task 2: Select and Run a One Sample Confidence Interval Analysis. For one expenditure variable, select and run the appropriate method for estimating a
- 21. parameter, based on a statistic (i.e., confidence interval method). Complete Table 2: Confidence Interval Information and Results, which follows the format outlined by Kozak and the course’s problem-solving approach, including: ○ Random variable stated in words ○ Confidence interval method, including rationale and assumptions ○ Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.). ○ Results obtained ○ Interpretation ➢ Task 3: Select Two Sample Hypothesis Test. Using the second expenditure variable (with the socioeconomic variable as the grouping variable), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample hypothesis test method). Complete Table 3: Two Sample Hypothesis Test Analysis, which follows the format outlined by the course’s problem-solving approach, including: ○ Hypotheses (null and alternative). ○ Two sample hypothesis testing method, including rationale and assumptions ○ Method used for analyzing data (i.e., web applets, Excel, TI calculator, etc.). ○ Results obtained. ○ Interpretation (i.e., Reject the null hypothesis OR Fail to
- 22. reject null hypothesis) NOTE: For this analysis, use all 30 data points for each variable (you may group the values by another variable, but you still must use all 30 data points). STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup - Instructions Page 2 of 4 Step 2: Write Up Results and Complete Part B of the Assignment #3 Template For this 1 to 2 page section, refer to the inferential statistics data plan and computations done for Part A of this assignment. Address the following areas: ➢ Introduction. Based on the scenario you submitted for the second assignment, provide a brief description of scenario, including the variables that were used in this analysis. Include a completed “Table 1: Variables Selected for Analysis to show the variables you selected for analysis. ➢ Data Set Description and Method Used for Analysis. Briefly describe the data set, using information provided with data set and write up in Assignment #2. Also describe what method(s) (i.e., free web applets, Excel, TI Calculator) you us ed to analyze the data.
- 23. ➢ Results. In this section, you will report the results of your inferential statistics data analysis. For the Confidence Interval Analysis, write one paragraph that includes: o Statistical method used, including rationale and whether assumptions were met. o Statistical Interpretation. The statistical interpretation is that the confidence interval has a probability (1−α, where α is the complement of the confidence level) of containing the population parameter. o Real World Interpretation. Explain the results in everyday language. Recommend reviewing the text and information from the classroom for examples on how to report results in everyday language. For the Two Sample Hypothesis Test Analysis, write one paragraph that includes: o Hypotheses that were assessed. See table below for example format: Example Format for Writing Null and Alternative Hypotheses, in Words Null Hypothesis: There is no significant difference in [insert variable name]
- 24. between [insert group 1 name] and [insert group 2 name] households. Alternative Hypothesis: ➢ For two-tailed (≠): There is a significant difference in [insert variable name] between [insert group 1 name] and [insert group 2 name] households. ➢ For one-tailed (>): [Insert group 1 name] has statistically significantly higher [insert variable name] than [insert group 2 name]. ➢ For one-tailed (<): [Insert group 1 name] has statistically significantly lower [insert variable name] than [insert group 2 name] STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup - Instructions Page 3 of 4 o Statistical method used, including rationale and whether assumptions were met. See table below for example format: Example Format for Writing Statistical Method with Rationale To determine whether the there was a difference in [insert household expenditure] between [insert names of two groups), a [insert name of hypothesis test used] was used. It was the
- 25. appropriate statistical method, because [insert rationale]. The assumptions were assessed [insert information about the assumptions assessed and whether they were met]. o Conclusion from the Results. This is where you state whether to reject Ho or fail to reject Ho including the p-value that was obtained. The rule is: if the p-value < α, then reject Ho. If the p-value ≥ α, then fail to reject Ho. o Real World Interpretation. Explain, in everyday language, the results. If any of the assumptions were not met, describe how it might affect conclusions. Address issues of Type I and/or Type II Error, where appropriate. Recommend reviewing the text and information from the classroom for examples on how to report results in everyday language. ➢ Discussion– Write one paragraph that summarizes the results of your findings and how they may be helpful to the person described in the scenario, when making a household budget. STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup - Instructions Page 4 of 4
- 26. Assignment Submission: Save the file that contains your completed Assignment #3 Inferential Statistics Analysis - Template as a pdf or docx using the following format: “LastName, First Name – Assignment3.” Submit it via the Assignments area in the LEO classroom in the “Assignment #3: Inferential Statistics Analysis and Writeup” folder. Part A: Prepare Data Plan, Analyze Data, and Complete Part A of the Template Selection of variables and completion of table 10% Selection and Calculation of Confidence Interval Analysi s: ● Selection of Appropriate Test and Rationale ● Assumptions ● Method Used and Calculation ● Conclusion ● Statistical Interpretation 20% Selection and Calculation of Two Sample Hypothesis Test: ● Research Question and Hypotheses ● Selection of Appropriate Test and Rationale ● Assumptions ● Method Used and Calculation ● Conclusion, including p-value ● Statistical Interpretation 20% Part B: Write Up of Results
- 27. Introduction and Description of Data Set 5% Confidence Interval. Summarized: ● Statistical method used, including rationale and whether assumptions were met ● Statistical Interpretation ● Real World Interpretation. 15% Two Sample Hypothesis Test. Summarized: ● Hypotheses ● Statistical method used, including rationale and whether assumptions were met. ● Conclusion from the Results. ● Real World Interpretation. 15% Discussion 5% Wrote clearly, concisely, and with few errors. Easy to understand. 10% University of Maryland Global Campus Assignment #3: Inferential Statistics Analysis and Writeup Identifying Information Student (Full Name):
- 28. Class: Instructor: Date: NOTE: Review the instructions; this file does not detail ALL requirements for this assignment. Remove all red-text instructions from this template prior to submission. Save the file as a word document or pdf with the title “Last Name, First Name – Assignment 3” (do not submit a rtf file). Part A: Inferential Statistics Data Analysis Plan and Computation Introduction: Variables Selected: Table 1: Variables Selected for Analysis Variable Name in the Data Set Variable Type Description Qualitative or Quantitative Variable 1: Socioeconomic Variable 2: Expenditure Variable 3: Expenditure
- 29. Data Set Description and Method Used for Analysis: Briefly describe the data set, using information provided with data set and write up in Assignment #2. Also describe what method(s) (i.e., free web applets, Excel, TI Calculator) you used to analyze the data. 1. Confidence Interval Analysis: For one expenditure variable, select and run the appropriate method for estimating a parameter, based on a statistic (i.e., confidence interval method) and complete the following table (Note: Format follows Kozak outline): Table 2: Confidence Interval Information and Results Name of Variable: State the Random Variable and Parameter in Words: Confidence interval method including confidence level and rationale for using it: State and check the assumptions for confidence interval: Method Used to Analyze Data: Find the sample statistic and the confidence interval: Statistical Interpretation: 2. Hypothesis Testing: Using the second expenditure variable (with socioeconomic variable as the grouping variable for making two groups), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample hypothesis testing method) and complete the following table (Note: Format follows Kozak outline):
- 30. Table 3: Two Sample Hypothesis Test Analysis Research Question: Two Sample Hypothesis Test that Will Be Used and Rationale for Using It: State the Random Variable and Parameters in Words: State Null and Alternative Hypotheses and Level of Significance: Method Used to Analyze Data: Find the sample statistic, test statistic, and p-value: Conclusion Regarding Whether or Not to Reject the Null Hypothesis: Part B: Results Write Up Confidence Interval Analysis: Two Sample Hypothesis Test Analysis: Discussion: STAT200: Assignment #3 - Inferential Statistics Analysis and Writeup Page 1 of 4