Unit 3 Assessment Objectives: Determine the appropriate inference method needed to investigate a statistical question. Demonstrate how assumptions are met for various inference methods. Calculate and interpret a confidence interval. Carry out a hypothesis test. Identify and describe Type I or Type II error. Develop statistical computing skills. Develop a scholarly/technical writing style for reporting inference results. Type your work (do not re-type the questions). Ensure that solutions, equations, tables or graphs are neatly sized and aligned on the page; they must be easy for the professor to identify and read. Points will be deducted for poor formatting. Conduct all hypothesis test at a 5% level of significance and construct 95% confidence intervals. Description of the Data The data represent 1000 records collected on residences in a large U.S. city who volunteered to participate. Several methods were used to collect the data (survey, observation, experiment). The variable definitions are as follows: Variable Code Type Identification ID Nominal Job type BC = blue collar Categorical WC = white collar Job satisfaction Job Sat Categorical 1 = Very satisfied 0 = A rating other than very satisfied Are you 65 or older? Senior Categorical Yes = is 65+ No = is not 65+ Length in minutes of your Call (min.) Continuous last mobile phone call. Score made on the simulation No Alcohol Continuous game without alcohol. Score made on the simulation Alcohol Continuous game with alcohol. Do you live in a single SFH Categorical family home? Yes = lives in a SFH 1 No = does not live in a SFH Random comparative experiment groupings for memory test Experiment measurement: Score on the memory test Group Categorical Placebo = Control group Ginkgo = Experiment group Memory Test Continuous Draw a Simple Random Sample Draw a simple random sample of size 250 from the Unit 3 Assessment Data. [In JMP open the file then go to Table > Subset.] Enter 250 for Random Sample Size and select OK. Save the sample as a JMP file and post it to the group's discussion board. All of your analyses must be conducted on the drawn random sample. 2 Scenarios Scenario 1 The individuals in the data set were given a survey asking them to classify their job type as either white collar (working in an office or similar type of professional environment) or blue collar (manual work or working in an industry). The survey also asked them to rate their job satisfaction. Is there evidence to suggest white collar and blue collar workers hold different conceptions of their work? That is to say, is the rate at which white collar workers responded \"very satisfied\" significantly different than the rate for blue collar workers. Scenario 2 Participants played a simulated game in which they performed various tasks while sober and the score for tasks successfully completed was recorded. Three days later, the participants played the game again this time after drinking alcohol. The score of tasks successfully completed after using alcohol was recorded. Is there evidence to suggest drinking alcohol impaired the participants' ability to perform the tasks? Scenario 3 A mobile phone carrier knows that the mean length of all calls for all of its customers in a certain city is 9.2 minutes. The company is thinking of offering seniors (65 or older) a discount as an incentive to attract new customers. A survey question asked participants to give the length of their last call, which they could read off their phone. The company wants to know if the evidence supports that the length of calls for seniors is about 9.2 minutes. Scenario 4 A researcher studied the effects of using the supplement ginkgo biloba for improving memory. Participants were randomly assigned to a treatment group that received the ginkgo supplement for one month or to a control group that received a sugar pill (placebo) for one month. At the end of the month, each participant's memory was assessed using a test requiring them to recall various items. Is there evidence to suggest gingko improves memory? Scenario 5 A developer is interested in building a new subdivision in the city where the participants live. The housing development will consist of single-family and apartment homes, and the developer wishes to keep with current data that suggests 71% of U.S. citizens prefer a single-family home. Is there evidence to suggest a significantly different proportion of people in the city prefer single family homes? Complete the Tables Read each scenario above and decide which method is to be carried out. Write the scenario number in the space provided above the table, then complete the table. Methods may be used more than once. Delete all unused sections. 3 Scenario [Insert Number]. One Sample Proportion Confidence Interval & Hypothesis Test Graph of the Data [INSERT GRAPH] Descriptive Statistics X Sample Proportion Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules Critical Region Method Decision Rule: P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 4 Scenario [Insert Number]. One Sample Proportion Confidence Interval & Hypothesis Test Graph of the Data [INSERT GRAPH] Descriptive Statistics X Sample Proportion Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules Critical Region Method Decision Rule: P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 5 Scenario [Insert Number]. One Sample Mean Confidence Interval & Hypothesis Test Graph of the Data [INSERT GRAPH] Descriptive Statistics Mean Standard Deviation Median Inter-quartile Range Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules Critical Region Method Decision Rule: P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 6 Scenario [Insert Number]. One Sample Mean Confidence Interval & Hypothesis Test Graph of the Data [INSERT GRAPH] Descriptive Statistics Mean Standard Deviation Median Inter-quartile Range Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules Critical Region Method Decision Rule: P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 7 Scenario [Insert Number]. Two Sample Proportions Confidence Interval & Hypothesis Test Descriptive Statistics X1 N1 X2 N2 Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 8 Scenario [Insert Number]. Two Sample Proportions Confidence Interval & Hypothesis Test Descriptive Statistics X1 N1 X2 N2 Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 9 Scenario [Insert Number]. Two Independent Sample Means Confidence Interval & Hypothesis Test Descriptive Statistics N1 Mean1 SD1 N2 Mean2 Graph of Sample 1 Graph of Sample 2 [INSERT GRAPH] [INSERT GRAPH] SD2 Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 10 Scenario [Insert Number]. Two Independent Sample Means Confidence Interval & Hypothesis Test Descriptive Statistics N1 Mean1 SD1 N2 Mean2 Graph of Sample 1 Graph of Sample 2 [INSERT GRAPH] [INSERT GRAPH] SD2 Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 11 Scenario [Insert Number]. Two Dependent Sample Means Confidence Interval & Hypothesis Test Graph of the Data [INSERT GRAPH HERE] Descriptive Statistics Mean Standard Deviation Median Inter-quartile Range Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules Critical Region Method Decision Rule: P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 12 Scenario [Insert Number]. Two Dependent Sample Means Confidence Interval & Hypothesis Test Graph of the Data [INSERT GRAPH HERE] Descriptive Statistics Mean Standard Deviation Median Inter-quartile Range Hypotheses Null Hypothesis Notation In Words (provide context) Alternate Hypothesis Notation In Words (provide context) Assumptions & Conditions Explain whether the necessary conditions are met for the method. Decision Rules Critical Region Method Decision Rule: P-value Decision Method Rule: Test statistic & P-value Test Statistic P-value Results Decision and its interpretation in context. Identify the type of error possible. Confidence Interval Endpoint Values In Words (provide context) 13