SUPPLEMENTARY EXERCISES for ... - WH Freeman

Section 2 43high school seniors is 452 to 470. Asked to explain the meaning of this interval, the studentsays, “95% of California high school seniors have SAT math scores between 452 and 470.” Isthe student right? Justify your answer.Section 2S6.8 Each of the following situations requires a significance test about a population mean µ.State the appropriate null hypothesis H 0 and alternative hypothesis H a in each case.(a) The mean area of the several thousand apartments in a new development is advertised to be1250 square feet. A tenant group thinks that the apartments are smaller than advertised. Theyhire an engineer to measure a sample of apartments to test their suspicion.(b) Larry’s car averages 32 miles per gallon on the highway. He now switches to a new motoroil that is advertised as increasing gas mileage. After driving 3000 highway miles with the newoil, he wants to determine if his gas mileage actually has increased.(c) The diameter of a spindle in a small motor is supposed to be 5 millimeters. If the spindle iseither too small or too large, the motor will not perform properly. The manufacturer measuresthe diameter in a sample of motors to determine whether the mean diameter has moved awayfrom the target.S6.9 In each of the following situations, a significance test for a population mean µ is called for.State the null hypothesis H 0 and the alternative hypothesis H a in each case.(a) Experiments on learning in animals sometimes measure how long it takes a mouse to find itsway through a maze. The mean time is 18 seconds for one particular maze. A researcher thinksthat a loud noise will cause the mice to complete the maze faster. She measures how long eachof 10 mice takes with a noise as stimulus.(b) The examinations in a large accounting class are scaled after grading so that the mean scoreis 50. A self-confident teaching assistant thinks that his students have a higher mean score thanthe class as a whole. His students this semester can be considered a sample from the populationof all students he might teach, so he compares their mean score with 50.(c) A university gives credit in French language courses to students who pass a placement test.The language department wants to know if students who get credit in this way differ in theirunderstanding of spoken French from students who actually take the French courses. Somefaculty think the students who test out of the courses are better, but others argue that theyare weaker in oral comprehension. Experience has shown that the mean score of students in thecourses on a standard listening test is 24. The language department gives the same listeningtest to a sample of 40 students who passed the credit examination to see if their performance isdifferent.S6.10 You have performed a two-sided test of significance and obtained a value of z = 3.3. UseTable D to find the approximate P -value for this test.S6.11 You have performed a one-sided test of significance and obtained a value of z = 0.215.Use Table D to find the approximate P -value for this test.