Please help with the following assignment (will give helpful rating):
AI CI '- Write a null and an alternative hypothesis for each of the following. Be sure to state each hypothesis in the context of the problem. A forestry textbook claims that the mean age of pine trees in Colorado is 3|! years. You think the age is greater than that. [2 points] . A brochure on anti-aging cream states that the mean age of people in the United States la 75 years. You doubt the claim, and you think it'a greater because the Information is out of date and the population of the elderly is growing. (2 points} . A llaheriea report states that the mean weight of trout in Lake standarderror is 3.4 pounds. You think the information is out of date, and that the population may have changed. (2 points:- . Acme Caterpillar Farm claims the mean length of their award-winning caterpillars is 8 oer-Itimetera. You've seen their caterpillars and you think the mean length must be diverts. (2 points) A theory predicts that the mean age of stars within a partimlar type of star cluster is 3.3 billion years, with a standard deviation of .4 billion years. (Their ages are approximately normally distributed.) You think the mean age is actually greater, and that this would lend support to an alternative theory about how the clusters were formed. You use a oomputer to randomly select the coordinates of 50 stars from the catalog of known stars of the type you're studying and you estimate their ages. You nd that the mean age of stars in your sample is 3.4 billion years. TO \"It whether the \"Militia" mean ie greater than 3.3 billion yeare, what would Val" null and alternative hypotheeee be? 3. cure to It!\" the hypotheeee In the context of the problem. {2 points) What teat would you plan to uae, how will the teat work, and what are the conditions neceeaery t0 III. the teat? Doee your Illl'tl meet those conditions? (2 points] Calculate your teat etetletlc and P-velue. Show your work, including the formulae you uae to ceiculete the eta'tlatic. [2 points) What'e your conclusion ualng e - .115? (2 points] Suppose VDLI doubt the assumption that the mean age Elf the stars IE 3.3- billion years, but you don't know whether the true mean age I! less or greater than 3.3 blllltll'l years. To tact. whether the population mean ie 3.3 billion yeara, what would your null and alternative hypotheaea be? {2 points) Whit teat wlll you uae, hlillillI will the teat work, end what Ire the condition neceaaary to uee the teat? Does your altuation meet thoee conditions? (2 points) C. Using the population and sample from question 2, calculate your test statistic and P-value. Show your work, including the formulas you used to calculate the statistic. (2 points) D. What's your conclusion, using a = .05? Compare your results to the previous conclusion, and explain the difference. Sketch the distribution of your sample mean, shading the area that represents your P-value. Label the value for the mean, and label the values for the bounds of the shaded area. (3 points)
