Simple statistics question.

A Statistics question- Please help me :(?

• Question 1. The melting point of each of 16 samples of a certain brand of hydrogenated vegetable oil was determined, resulting in x ̅ = 94.32 and s = 2.80. Test H0: µ = 95 versus H1: µ ≠ 95 using a two-tailed test with a significance level of 0.01. Question 2. A sample of 36 speedometers of a particular brand is obtained, and each is checked for accuracy at 55 mph. The resulting sample average and sample standard deviation are x ̅ = 54.5 and s = 1.5. Let µ be the true population average speedometer reading when the actual speed is 55 mph. Does the sample evidence suggest strongly that µ ≠ 55? Use a significance level of 5% for the test. Question 3. A random sample of 40 recorded speeds is obtained from cars traveling on a section of Highway 405 in Los Angeles. The sample has a mean speed of 68.4 mph and a standard deviation of 5.7 mph. Use a 5% significance level to test the claim that the mean speed of all cars is greater than the posted speed limit of 65 mph. Question 4. A random sample of 25 cigarettes from a normally-distributed population of filtered 100 mm cigarettes is obtained, and the tar content measured. The sample has a mean of 13.2 mg and a standard deviation of 3.7 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1, which is the mean for unfiltered king size cigarettes. What do the results suggest about the effectiveness of the filters?

• Answer:

  Ans: 1. z = (94.32 - 95)/(2.80/sqrt(16)) = -0.9714 critical z = +/- 2.58 Hence, computed z (-0.9714) is within (-2.58, +2.58). Fail to reject Ho. From TutorTeddy