Discuss the following problems:
Q1. A police officer claims that the average speed of cars on a certain stretch of highway is greater than 70 miles per hour--thus more patrols needed. We decide to conduct a hypothesis test at the 1% significance level to test the officer's claim. We randomly select and record the speeds of cars passing by. The sample data (in miles per hour) is given to the right. Speed of Cars
72 66 65 60 67 67
62 72 77 68 70 75
78 80 67 76 72 75
80 78 78 79 79 73
(a) Give the null and alternative hypotheses for this situation in mathematical notation. 74 80 69 77 63 73 64 64 76 70 63 70
(b) Based upon a 1% level of significance, determine the critical value(s) associated with this hypothesis test.
(c) Determine the sample's test statistic.
(d) State a final conclusion regarding the results of the hypothesis test. Make sure your statement is tied to the context of the problem (speeds of cars on this stretch of highway).
Q2. It has been reported that 60% of adults plan to vote in the November election. To test this claim, a researcher surveyed 75 people and found that 54 say they will vote in the November election. Conduct a hypothesis test at the 5% significance level to test the claim that 60% of adults will vote in the November election. (HINT: In this problem, you are trying to decide if your sample provides evidence that the percentage of adults who attended a musical play in the past year is different than 60%.)
(a) List the null and alternative hypotheses for this test.
(b) Determine the value of the sample's test statistic.
(c) Determine the critical value(s).
(d) Detemine the P-value.
(e) Give a final interpetive sentence tied to the context for the hypothesis test results.