Name: ______________________________________________Points you missed on the test (out of 22)_______Signature of Learning Assistant or Instructor:Instructions: If you missed 5 points (not five questions!) or fewer, you need only answer the questions you missedand complete problem 11 (which was originally extra credit). If you missed more than 5 points, you should re-do theentire test. You will receive 5 points for corrections which will be added to your test scores after the final exam. Yourtotal score may not exceed 100%.DUE DATE: May 6, 5:30 PM——————————————————————————————————————1. What is a sampling distribution?2. What is the special name for the standard deviation of a sampling distribution?____________________3. For a sampling distribution of the proportion from a population with population proportion p,What is the mean of the distribution?What is the standard error of the distribution?4. For a sampling distribution of the mean from a population with population mean μ and standarddeviation σ ,What is the mean of the distribution?What is the standard error of the distribution?5. How do you determine (theoretically, without simulation) if the sampling distribution of a sampleproportion is likely to be approximately Normal?6. We usually assume that the sampling distribution of the sample mean is approximately Normal if thesample size is at least 30.Under what conditions would we be safe in assuming Normality for a smaller sample size?Under what conditions might we need a larger sample size?7. You showed by simulation that the standard error of a sampling distribution would decrease if youincreased the sample size. Show how the formula for the standard error can be used to confirm thistheoretically.8. By what factor would you have to increase the sample size to cut the standard error in half? Provideevidence for your answer. You may use empirical evidence from your lab or theoretical evidence byusing the formula, as we did in class.9. When using the StatKey applets, you can change two numbers:the sample SIZEORthe NUMBER of samplesYou increase one of them to try to produce a better approximation to the true sampling distribution and abetter estimate of the true standard error. Which one? __________________You increase the other to produce an entirely different sampling distribution with a different (smaller)standard error. Which one? ___________________________Sp16_43_U7v110. During the 2008 presidential election, newspapers reported that Barak Obama received 40% of the whitemale vote. If this is true, what is the probability that a random sample of 1000 white male voters had asample percentage of more than 42% voting for Mr. Obama? Show all the steps for using the Normalmodel to answer this question. (a) First verify that the Normal model is appropriate. (b) Find the standarderror. (c) Find the Z-score and interpret it. (d)Then find the probability an applet. Make a sketch of thedistribution you used. Shade the area representing the probability you found.11. A sampling distribution is shown forthe proportion of US citizens over 15years old who have never been married,using the data from the 2010 US Censusand random samples of size n = 500.a). What does one dot in the dotplotrepresent?b) Use the sampling distribution toestimate the proportion p of all US citizens over 15 years old who have never been married. __________________c) Verify using the formula that the sampling distribution is approximately Normal.d) From the dotplot, it appears that it would be quite unlikely to obtain a sample of size 500 from thispopulation with a sample proportion of 0.27 or less. Verify this theoretically by assuming that the samplingdistribution is approximately Normal (as you showed in part c) and finding the probability of obtaining such asample Show all your work. If you used an applet, make a sketch.