project 8 B

Progress Check

Use this activity to assess whether you can:

• Determine when to use a hypothesis test or a confidence interval to draw a conclusion about a population mean.
• Construct a confidence interval to estimate a population mean when conditions are met.
• Under appropriate conditions, conduct a hypothesis test about a population mean and state the conclusion in context.
• Under appropriate conditions, conduct a hypothesis test about a difference between two population means and state a conclusion in context.

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Directions

WARNING: The directions for Unit Projects differ from the directions for homework and lab assignments.

Use the drop-down menu to learn about the four steps needed to complete this assignment.

Four steps to complete the assignment

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Data

From this point forward, all links in this assignment open in a new tab.

• Login and open StatCrunch (directions). My account on StatCrunch: User Aobeeda2003
  
• Open your IAT sample data set in StatCrunch (directions).

ompt

QUESTION 1

1. 1. Which IAT data set are you working with?
   2. Use StatCrunch and your unique IAT sample to estimate the mean age for the population of IAT participants at the 90% confidence level. Copy the contents of your StatCrunch output window and paste them into your response. (No need to type anything here – just copy and paste the contents of your StatCrunch output window.)
   3. Are conditions met to estimate the mean age for the population of IAT participants? (Be sure to support your answer as demonstrated throughout Unit 8.)
   4. State the confidence interval, and then interpret the confidence interval in context.
   5. What is the margin of error (MOE)?
   6. Which would be more accurate, the 90% confidence interval you found or an 85% confidence interval? Briefly explain. Which would be more precise? Briefly explain.

QUESTION 2

At the end of 2020, the mean age of the U.S. population was estimated to be 38.5 years old. You are tasked with determining whether the mean age of the population of IAT participants (for your chosen IAT data set) differs from the mean age of the U.S. population.

1. 1. Let $�$be the mean age of the population of IAT participants for your chosen IAT data set. State the hypotheses (symbolically and in words). Include a clear description of the populations and the variable.
   2. Use StatCrunch to create a histogram for the age distribution in your unique IAT sample. Download the StatCrunch output window and embed your histogram with your response. Can we safely use the t-test with your IAT sample? Explain.
   3. Perform the t-test using StatCrunch. Copy the information from the StatCrunch output window and paste it into your response.
   4. Based on the P-value, state your conclusions in context. Use a 5% level of significance. (NOTE: Since StatCrunch correctly calculates the P-value for either a one-tailed or a two-tailed test, you do not need to change the StatCrunch P-value.)
   5. Using the context of this scenario, explain the meaning of each of the following items from the StatCrunch output for the hypothesis test.
      Std. Err (standard error)
      T-stat (T-score)
      P-value

QUESTION 3

Below are the variables for Question 3. For all data sets, the categorical variable is the explanatory variable, and the quantitative variable is the response variable.

GENDER-CAREER IAT VARIABLES FOR QUESTION 3 ONLY

Open for the Gender-Career variables

GENDER-SCIENCE IAT VARIABLES FOR QUESTION 3 ONLY

Open for the Gender-Science variables

RACE IAT VARIABLES FOR QUESTION 3 ONLY

Open for the Race variables

SEXUALITY IAT VARIABLES FOR QUESTION 3 ONLY

Open for the Sexuality variables

WEAPONS IAT VARIABLES FOR QUESTION 3 ONLY

Open for the Weapons variables

WEIGHT IAT VARIABLES FOR QUESTION 3 ONLY

Open for the Weight variables

• Choose only one of the categorical variables listed for your IAT data set and note the two groups for your chosen categorical variable.
• Here is the question to be investigated for the two groups in your chosen categorical variable.
  Do the population of IAT participants in one group score higher on the IAT test than the population of IAT participants in the other group?

TO ANSWER THE QUESTION WE ARE INVESTIGATING, RESPOND TO EACH OF THE FOLLOWING

1. 1. Use StatCrunch to determine the sample size and sample mean, $\overline{�}$, for the two groups in your chosen categorical variable (directions).
      • Copy your StatCrunch output table and paste it into your response. Then relabel the categorical variable groups with the appropriate word(s), i.e. replace the group numbers with the appropriate word(s) to describe the group (see the Categorical Variable section above for your data set).

• 1. • Which of the two groups has the smallest sample mean? Which has the largest sample mean?
  2. Let ${�}_1$ be the population mean for the group with the largest sample mean. Let ${�}_2$ be the population mean for the group with the smallest sample mean. State the null and alternative hypotheses (symbolically and in words). Include a clear description of the populations and the variable.
  3. To test your hypotheses, is it appropriate to use the two-sample T-test? If so, explain why and provide any supporting evidence. If not, start over and choose the other categorical variable listed with your chosen IAT data set.
     • WARNING: If it is not appropriate to use the two-sample T-test for either of the categorical variables listed with your IAT data set, something may be wrong. Stop and contact me as soon as possible.
     • Proceed only if it is appropriate to use the two-sample T-test.
  4. Use StatCrunch to carry out the test (directions).
     Copy the content in the StatCrunch output window (text and the table) and paste it into the textbox as your response to this item.
  5. Use a 5% significance level to state a conclusion. Be sure to state your conclusion in context and in terms of what a “more positive score” on the IAT means for your data set. (Hint: in the variables section above, click on the variable descriptions link for your data set. The variable descriptions page opens in a new window. Review the Interpreting the IAT section at the top of that page.)

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StatCrunch Directions

Here is a PDF document with all StatCrunch directionsLinks to an external site. (opens in a new tab).

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Unit 8 Project Discussion Board

Use the Unit 8 Project discussion board (opens in a new tab) to ask questions or provide feedback about this project.

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Review Feedback

• Instructor feedback is only available after an assignment is graded.
• Use these directions (opens in a new tab) to learn how to review feedback.

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Click the “Next” or > button to continue.

Content by Cuyamaca College math faculty and licensed under the Creative Commons 4.0 International LicenseLinks to an external site..

Rubric

Unit 8 Project

Unit 8 Project

Criteria	Ratings	Pts
This criterion is linked to a Learning OutcomeQuestion 1aIAT data set is identified	1 pts Complete 0 pts Incomplete	1 pts
This criterion is linked to a Learning OutcomeQuestion 1bStatcrunch was used to correctly create a 90% confidence interval for the mean age.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 1cSteps are correctly shown for checking conditions.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 1dThe confidence interval is correctly stated and interpreted in context.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 1eThe margin of error is correctly identified.	3 pts Complete 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 1fCorrectly identified which confidence interval (90% vs. 85%) is more accurate and which is more precise. Explanations included.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 2aHypotheses are provided in symbols and words. Includes a clear description of the populations and the variable.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 2bA histogram was created using the correct variable. Correctly addressed the question “Can we safely use the t-test with your IAT sample?” Explanation included.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 2cStatCrunch t-test is correct.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 2dThe conclusion is correctly stated in context, with reference to the p-value.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 2eThe meaning of the standard error, t-stat, and p-value is correctly provided in context.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 3aStatCrunch output table is correctly provided. Categorical variable groups were relabeled with appropriate words. Correctly identified the group with the smallest sample mean and largest sample mean.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 3bHypotheses are correctly stated symbolically and in words. Includes a clear description fo the populations and the variable.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 3cExplanation of why the two-sample t-test is appropriate and supporting evidence is provided.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 3dStatCrunch output for the two-sample t-test is correctly provided.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeQuestion 3eThe conclusion is correctly stated in context. Reference to what a “more positive score” on an IAT means for your data set is provided.	3 pts Complete 2 pts Partial Credit 0 pts Incomplete	3 pts
This criterion is linked to a Learning OutcomeSelf-EvaluationThe final draft begins (or ends) with a self-evaluation of your first draft. The self-evaluation describes how you demonstrated attainment of the learning objectives in the “Progress Check” section of the assignment, OR what you needed to correct in order to demonstrate attainment of the learning objectives.	4 pts Complete 2 pts Partial Credit The self-evaluation does not describe how you demonstrated attainment of the learning objectives in the “Progress Check” section of the assignment, or what you needed to correct in order to demonstrate attainment of the learning objectives. 0 pts Incomplete No self-evaluation of your first draft is included with your final draft. Or, you did not commit a good-faith effort on your first draft and therefore your self-evaluation is not applicable.	4 pts
Total Points: 5 My account on StatCrunch: User Aobeeda2003

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