Which IAT data set are you working with?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 it into your response. (No need to type anything here - just copy and paste the contents of your StatCrunch output window.)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.)State the confidence interval, and then interpret the confidence interval in context.What is the margin of error (MOE)? 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 2At 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.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.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.Perform the t-test using StatCrunch. Copy the information from the StatCrunch output window and paste it into your response.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.) Using the context of this scenario, explain the meaning of each of following items from the StatCrunch output for the hypothesis test.Std. Err (standard error)T-stat (T-score)P-valueQuestion 3Prepare to work through Question 3See the Variables for Question 3 Only section above to learn which variables to use for your chosen IAT data set.Choose only one of the categorical variables listed for your chosen 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 followingUse StatCrunch to determine the sample size and sample mean, , for the two groups in your chosen categorical variable (directions).Copy your StatCrunch output table and paste 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).Which of the two groups has the smallest sample mean? Which has the largest sample mean?Let 𝜇1μ1 be the population mean for the group with the largest sample mean. Let 𝜇2μ2 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.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.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. 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. Gender-Career IAT Variables for Question 3Quantitative VariableIAT-Gender-Career: Score on the Gender-Career IATCategorical Variable (choose one)Children: Are you currently the parent or guardian of a child (or children) under 18 living in your home? 1=Yes; 2=No ORBirth-Gender: 1=Male; 2=FemaleORPrimary-Job: During your youth, did your primary caregiver have a job outside the home? 1=Yes; 2=No

Problem Statement: Given the following right triangle, find cosθ, sinθ, tanθ, secθ, cscθ, and cotθ. Do not approximate: Find exact answers. Show all of your work and explain steps as necessary. Prompt: Use the provided template to solve the trigonometric functions problem above, and illustrate your process by addressing each of the following elements: I. Establish a context for the problem by explaining in your own words the course principles that apply: What are the relationships between theta and the lengths of the sides of the triangle? Be sure to correctly use the appropriate terminology in your explanation. II. Apply the mathematical process to solve the problem: A. Use the Pythagorean theorem to find the third side of the triangle. B. Write out the six trigonometric functions related to theta in exact form. III. Clearly state the answer using appropriate precalculus notations.Rubric and Milestone Template Attached

What is it meant by the term “parameter of a population”? Explain why a population can be represented by a random variable.What is a point estimate, and an unbiased point estimate? Explain how the sample mean can be an unbiased estimate of the population mean. How do you justify that the sample variance is an unbiased estimate of the population variance? What is the sampling requirement in the latter case? Provide a numerical example of estimating the mean, the variance, and the standard deviation.Please define each of the following terms, discuss applicability and significance of each: sample statistic, standard error, sampling distribution, and central limit theorem. Include hypothetical examples for better clarity. What is the z statistic and what qualifies a statistic to be z statistic based on the central limit theorem and the basic properties of normal distributions? What are the limitations of the central limit theorem, and how some of these limitations are bypassed? For example, the z statistic as the sampling distribution in estimating a proportion.What is the sampling distribution in estimating the variance of a population? What are the properties of this distribution?What is the alternative of z statistic for normally distributed populations which eliminates some limitations of the central limit theorem? How this sampling distribution is constructed as a combination of a z distribution and a chi squared distribution? What are the properties of this distribution? (To provide numerical examples to answer questions mentioned above, for example, in the third item above, you can use the Excel function RAND to generate a sample of a uniform random variable, and the combination of RAND and NORM.INV to generate a sample of a normal random ).Please use APA format with peer reviewed references .