1.

Are you smarter than a second grader? A random sample of 55 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x =46. Assume the standard deviation of test scores is 6: 18. The nationwide average score on this test is 50. The school superintendent wants to know whether the second graders in her school district have different math skills than the nationwide average. Use the 0i=0.05 level of significance and the Pvalue method with the TI84 Plus calculator. Part 1 of5 (a) State the appropriate null and alternate hypotheses. H02 ' u = 50 ' H1 2 ' p 7E 50 ' This hypothesis testis a 'twotailed V test. Part:1/5 - Part20f5 (b) Compute the value of the test statistic. Round the answer to two decimal places. z=l l X 5) Calibrating a scale: Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST) in Washington, DC. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be 6:2. They weigh this weight on the scale 47 times and read the result each time. The 47 scale readings have a sample mean of;=999.1 grams. The calibration point is set too low if the mean scale reading is less than 1000 grams. The technicians want to perform a hypothesis test to determine whether the calibration point is set too low. Use the (1:0.01 level of significance and the Pvalue method with the TI84 Plus calculator. Part10f5 o (a) State the appropriate null and alternate hypotheses. H0: i u = 1000 i H1: i 1.1