The key steps to tests of significance are to state H0 and HA, calculate the test statistic, compute the pvalue, and make a conclusion based on the given significance level. If you input the hypotheses and the summary statistics into Minitab Express, Minitab Express will output the test statistic and p-value and you will not have to do any complex calculations. Keep in mind that the results obtained from software are not meaningful unless the correct null and alternative hypotheses are determined. If the question requires a test of significance, your solution should clearly show the four steps to the test. In addition, you should show that you have checked that the conditions for inference are met. Step 1: State the null and alternative hypothesis. (Use “mu” or the symbol µ.) Step 2: Calculate the test statistic. Step 3: Find the p-value. Step 4: State your conclusion in the context of the problem. (Do not just say “Reject H0” or “Do not reject H0.”) If the question requires a confidence interval, be sure to make a statement about the confidence interval in context of the problem.
Question 1. Fuel Economy for Midsize Cars. The Department of Energy provides fuel economy ratings for all cars and light trucks sold in the United States. The Minitab Express file for this problem contains the estimated miles per gallon for highway driving for the 205 cars classified as midsize in 2014. Use this data set to test the claim that manual transmission vehicles get better highway mileage at the 10% significance level.
Question 2. Mary has developed a new way of teaching story problems in sixth grade arithmetic. She used her method on a random sample of 50 sixth graders from her school. An independent random sample of 50 sixth graders was taught to solve story problems by a traditional method. All students were given the same test. Mary's students had an average score x1 = 82 (out of 100 possible points) with standard deviation s1 = 8.5. The other group had an average x2 = 75 with standard deviation s2 = 10.0. Does the new method improve performance on story problems? (Use a 5% significance level.)
Question 3. A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given below. At the 5% level of significance, test the claim that the sensory measurements are lower after hypnotism (scores are in cm. on a pain scale). Assume sensory measurements are normally distributed. Note: You do not need to type these values into Minitab Express; the data file has been created for you.
Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6
After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0
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