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(answered) – 1 STA100A and STA100B Homework 8 Due at the beginning of class on


(answered) – 1 STA100A and STA100B Homework 8 Due at the beginning of class onDescriptionSolution downloadThe QuestionBelow is my homework attached, it has 6 questions. It is pretty self-explanatory1STA100A and STA100B Homework 8Due at the beginning of class on February 29, 2016Write your name and student IDon the left side at the top of the ?rst page.Write the homework number in the middle at the top of the ?rst page.Write your section number on the right side at the top of the ?rst page.Staple all pages.If your homework is on paper pulled out of a notebook,cut o? all of the fringes (from the torn horizontal threadsthat attached the paper to the notebook).Percentage lost if youdon?t follow the rule2%2%2%2%2%For example, for homework 8 if your name is John Smith, your student ID is 123456789, andyou are in section A01, then the top of your ?rst page should look like thisJohn Smith123456789Homework 8A01and if you are in section B01, then the top of your ?rst page should look like thisJohn Smith123456789Homework 8B01Be kind to the grader.? make sure you write your name clearly (so it is easy to read)? write neatly? circle all ?nal answers (so they are easy to ?nd)Round all test statistics and con?dence intervals to two digits after the decimal point. Roundall p-values to four digits after the decimal point.21. Suppose systolic blood pressure of adults has a normal distribution with mean 130 andstandard deviation 35.Research question: Do statistics teachers have a have a di?erent average systolic bloodpressure than 130?A random sample of 100 statistics teachers is obtained and the mean is 135. Assumethe population standard deviation for statistics teachers is known: ? = 35.Let ? be the average systolic blood pressure for the population of statistics teachers.The null and alternative hypotheses are as follows.H0 : ? = 130 null hypothesisHA : ? = 130 alternative hypothesisConduct a hypothesis test with ? = 0.05 using the following steps.(a) Calculate the test statistic.(b) What is the critical value?(c) Do you reject or fail to reject the null hypothesis. How did you make your decision?2. The level of calcium in the blood in adults has mean 9.5 milligrams per deciliter andstandard deviation 0.4. Blood calcium is measured in a sample of 180 adults fromGuatemala and the mean is 9.58. We would like to test if the calcium levels of adultsin Guatemala di?ers from 9.5. De?ne ? as the population mean for all adults inGuatemala.(a) State H0 and HA .(b) Calculate the p-value. Assume that 0.4 is the known population standard deviation for adults in Guatemala. Use the following R command to calculate thep-value.2*(1-pnorm(abs(teststatistic)))Where teststatistic is the test statistic and abs(teststatistic) is the absolute valueof teststatistic.Since this is two sided the p-value is 2P(Z > |teststatistic|). The functionpnorm(X) give the area to the left of X in the standard normal distribution.(c) If ? = 0.05 does the data provide evidence in favor of HA ? How did you makeyour decision?(d) Give a 95% con?dence interval for the mean calcium level ?.Notice that we are con?dent ? is very close to 9.5. This illustrates the fact thata test based on a large sample size (n=180 here) will often declare even a smalldeviation from H0 to be statistically signi?cant, but the di?erence may not beclinically important.33. Suppose for statistics teachers and biology teachers systolic blood pressure is normallydistributed with standard deviation 35. To test if statistics and biology teachers havedi?erent systolic blood pressure a random sample of 200 statistics teachers and another random sample of 160 biology teachers is taken and their systolic blood pr