0n Route 19 there is a trafc light that allows for crosstrafc from Baker Avenue, a minor side street. Because Route 19 is a busy 4lane highway, the light is supposed to give Route 19 a green light 30% of the time, a yellow light 5% of the time, and a red light 15% of the time. An inspector thinks that the programming may be incorrect and that the distribution differs from the intended distribution. To investigate, he sets up a camera, which snaps a picture of the light at 150 randome selected times. Here are the results: Color Green Yellow Red Count 112 9 29 Do these data provide convincing evidence that the light's programming is incorrect? Use a: = 0.05. STATE: Place 2 appropriate hypotheses in each box. Leave the 4 incorrect hypotheses in the Answer Bank. _;MWW The light is functioning according to the intended distribution. Pam = 0-39: PYer = 0-55: lled = 0-15 pom = i FYcllaw = ; pm | The colors red, yellow, and green are not uniformly dish-ibuted for this trafc light. | [ The light is not functioning according to the intended distribution. l I The colors red, yellow, and green are uniformly distributed for this trajc Ii ght. l | At least two of the proportions are not as they are supposed to be. | PLAN: Name the test: ChiSquare Test for Goodness of Fit ' RANDOM: We have a random sample of 150 times for which the color of the trafc light is recorded. 7 10%: The 10% condition is not met. ' What is the expected count for each color if H0 is true? {Do not round) Expected Count for Green = Expected Count for Yellow = Expected Count for Red 2 Are all of the expected counts at least 5? I , I 2 X = (Enter at least 2 decimal places) Pvalue = I , I CONCLUDE: Because the Pvalue I - I cc 2 0.05. the correct decision is to I - I. We I convincing evidence that the trafc light , functioning as it is supposed to