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Math 200 – Project 2This project will cover topics from chapters 7 through 10. All papers will need to be submitted . You will be turning in a paper that should include section headings, graphics and tableswhen appropriate and complete sentences which explain all analysis that was done in additionto all conclusions and results. All work should be your own. Plagiarism will result in a projectscore of 0.You will be performing an analysis on female heights, given of set of 30 heights that wererandomly obtained. For this project, it is necessary to know that the average height for womenis assumed to be 65 inches with a standard deviation of 3.5 inches. You will use these numbersin some of your calculations.Steps:1. Download the data . This is the data that you will use throughout thisproject.2. Find Elizabeth in the data and, given the population mean and standard deviation,calculate:a. The z-score for Elizabeth (easiest to be done by hand).b. The probability that a randomly selected female is shorter than Elizabeth.c. The probability that a randomly selected female is taller than Elizabeth.d. Interpret each of these in a sentence (3 full sentences).e. HINT: for this step you should use the mean and standard deviation that aregiven in the paragraph above “Steps”. You should not use a sample mean orsample standard deviation calculated from the data given.3. As you know, a random sample of 30 women’s heights was obtained. Describe thesampling distribution. Use a full sentence here to describe the sampling distribution.HINT: See the Chapter 8 Lecture Notes Key or the Chapter 8 video lecture if you arestuck. You will not use the raw data yet.4. In StatCrunch or Excel, find and state the mean of the 30 women’s heights that wereprovided (round to two decimal places). Then (using the values from step 3), calculatethe probability that a random sample of 30 women’s heights would result in a meanthat was the value you found or more. Use this probability in a full sentence.5. Explain how what you just calculated in step 4 relates to the question you were asked instep 2c. Why is the probability in step 4 lower than that in step 2?6. For this step, please work under the assumption that we do not know the populationmean and standard deviation (and in fact, if we are running this test, it means that weare not sure of these values). Construct a 95% confidence interval for the average heightof a female. Interpret this confidence interval. HINT: You can use the “with data” optionin StatCrunch to do this calculation.Math 200 – Project 27. It is a researcher’s belief that the average height of females has increased since theaverage value of 65 inches was reported. Using the sample of 30 female heights,conduct a hypothesis test at the .05 level that tests whether or not this researcher mightbe correct. You must state the null and alternative hypotheses as well as the p-value andan interpretation of what this means. HINT: You can use the “with data” option inStatCrunch to do this calculation.8. How do the results from steps 6 and 7 relate to one another? HINT: does the true mean(given above these steps) lie in the interval found in step 6? How is this confirmed bythe result in step 7?9. Put everything together into an organized paper and submit it