Question 1 [10 marks] The Agriculture Department of a certain country reported that the average coffee consumption in the country, in 2014, was 26.0 gallons per person. A recently taken random sample of 400 residents of the country found a mean coffee consumption of 26.7 gallons with a sample standard deviation of 6.8 gallons. Assuming that the population of coffee consumption is normally distributed, test, at the 10% level of significance, whether the mean coffee consumption is different from the reported 26.0 gallons, by answering the following: (a) State the null and alternative hypotheses for the test. (b) Calculate the test statistics. (c) Determine the rejection region(s) for the test. (d) State the conclusion for the test giving reasons for your answer.
Question 2 [10 marks]Six months after graduating from college, randomly selected graduates were surveyed to determine their level of job pressure. The data was inputted into MINITAB Version 17.0 for analysis to determine whether level of job pressure is independent of gender. The following output, Exhibit 1, was generated using MINTAB: INTRODUCTION TO STATISTICS ECON1005 – Academic Year 2014/2015, Semester II Page 28 of 30 Exhibit 1 Chi-Square Test for Association: Age (years), Degree of Job Pressure Rows: Age (Years) Columns: Degree of Job Pressure Low Medium High All Less than 20 22 18 24 64 20.84 21.58 * 0.06424 0.59346 0.27173 20 - 39 52 48 46 146 47.55 49.23 49.23 0.41687 0.03054 ** 40 - 59 60 65 61 186 60.57 62.71 62.71 0.00545 0.08343 0.04677 60 and Above 36 45 45 126 41.03 42.48 42.48 0.61768 0.14915 0.14915 All 170 176 176 522 Cell Contents: Count Expected count Contribution to Chi-square Chi-Square = 2.640, DF = ***, P-Value = 0.852
(a) State the null and alternative hypotheses for the test. (b) Determine the missing values “*”, “**” and “***”. (c) State the conclusion for the test giving reasons for your answer. Total marks 20 [Graded out of 4]