# Mathematics Question

Question 1 A sample of 36 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level: H0: μ = 50 H1: μ ≠ 50 a. Is this a one- or two-tailed test? b. What is the decision rule? c. What is the value of the test statistic? d. What is your decision regarding H0? e. What is the p-value? Question 2 /4 A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level: H0: μ ≤ 10 H1: μ > 10 a. Is this a one- or two-tailed test? b. What is the value of the test statistic? c. If the decision rule is to reject Ho when z > 2.33, what is your decision regarding H0? Question 3 /8 A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the 0.08 significance level: H0: μ1 – μ2 ≤ 0 H1: μ1 – μ2 > 0 a. This is a one-tailed or a two-tailed test? b. State the decision rule. (Hint: reject H0 if z is “greater than”/”less than” x…) c. Compute the value of the test statistic. d. What is your decision regarding H0? e. What is the p-value? Question 4 /6 The following sample observations were randomly selected: X: 4 5 3 6 10 Y: 4 6 5 7 7 a. Determine the regression equation. b. Determine the value of Y’ when X is 7 Question 5 /8 The owner of Maumee Motors wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at Maumee Motors last year: Car Age (years) Selling Price (\$ thousands) 1 9 8.1 2 7 6 3 11 3.6 4 12 4 5 8 5 6 7 10 7 8 7.6 8 11 8 9 10 8 10 12 6 11 6 8.6 12 6 8 a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable, and which is the independent variable? b. Determine the regression equation. c. Estimate the selling price of a 10-year-old car.