(answered) – 1 STA100A and STA100B Homework 7 Due at the beginning of class onDescriptionSolution downloadThe QuestionMight need to use R studio for one question. I have attached my homework assignment below1STA100A and STA100B Homework 7Due at the beginning of class on February 22, 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 7 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 7A01and if you are in section B01, then the top of your ?rst page should look like thisJohn Smith123456789Homework 7B01Be 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 con?dence intervals to two digits after the decimal point. Round all p-values tofour digits after the decimal point.For this homework you may calculate the 95% con?dence intervals using a calculator orusing R. You may also calculate the 90% con?dence intervals using a calculator, but still useR to get the critical value (if you look it up in the Z table it won?t be exact). Use R forcalculating p-values.The R function pnorm(a,mean=b,sd=c) gives the area to the left of a under a normal curvewith mean b and standard deviation c. If you leave out the mean and standard deviationthe default values are mean=1 and sd=0, so pnorm(a) gives the area to the left of a undera standard normal curve.The R function qnorm(a,mean=b,sd=c) gives the value q such that P(Y < q) = a where Yhas a normal distribution with mean b and standard deviation c. The value of a must bebetween 0 and 1. If you leave out the mean and standard deviation the default values aremean=1 and sd=0, so qnorm(a) gives q such that P(Y < q) = a where Y has a standardnormal distribution. The q in the function is for quantile, which has the same de?nition aspercentile except that it ranges from 0 to 1 instead of 0 to 100.21. Suppose systolic blood pressure of adults has a normal distribution with mean 130 andstandard deviation 35.Research question: Do statistics teachers have a higher average systolic blood pressurethan 130?A random sample of 100 statistics teachers is obtained and the mean is 135. (Thepopulation standard deviation is known, so we use Z for critical values.)Let ? be the average systolic blood pressure for the population of statistics teachers.The null and alternative hypotheses areH0 : ? = 130 null hypothesisHA : ? > 130 alternative hypothesis(a) Calculate a one-sided (lower bound) 95% con?dence interval.s=35n=100se=s/sqrt(n)ybar=135#ONE-SIDED CRITICAL VALUEalpha=0.05Zcrit=qnorm(1-alpha)Zcrit#ONE SIDED (LOWER BOUND) CONFIDENCE INTERVALL=ybar-Zcrit*seL(b) For ? = 0.05, does the con?dence interval you calculated in (a) provide evidencethat the population mean systolic blood pressure of statistics teachers is greaterthan 130 (that is evidence in favor of the alternative hypothesis)? How did youmake the decision yes or no?(c) Calculate a one-sided (lower bound) 90% con?dence interval.(d) For ? = 0.1, does the con?dence interval you calculated in (c) provide evidencethat the population mean systolic blood pressure of statistics teachers is greaterthan 130? How
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