1) The null and alternative hypotheses, written using proper notation (2 points)2) The test statistic calculation showing:a. For the first problem, show the letter of the test statistic (chi-square or F), the formula for the test statistic, the numbers filled into the formula, and the final result. Round y2 test test statistics to three decimals; round Fest test statistics to two decimals. (3 points)b. For the second problem, show one example calculation of each type, and then fill in the calculation tables. You do not need to write out repetitive calculations. Keep four decimals on intermediate calculations. The test statistic can be rounded to three. (5 points)3) The rejection step showing BOTH the -value approach (2 points) AND the CV approach (2 points). You are not required to draw the rejection diagram unless you want to. You must show the proper p-value and proper CV or CVs, and the rejection rule (whether in numbers or with the diagram) that led vou to your decision about the null hypothesis. State what happened to the null and the alternative hypotheses to get full credit.4) Interpret the test result, referencing the alpha significance level (or percent confidence level), and answering all questions asked. (3 points)

1. (12 points) A manufacturer has been implementing a just-in-time inventory system for its production line. The final product requires a hinge to be installed at a particular station on the assembly line. Ideally, the next hinge would arrive at the station just when the operator needed it. However, due to various factors, some buildup of hinges at the station is to be expected. Of concern is the variance of the inventory of hinges. The company wants to ensure that the variance of hinge inventory is 30. If the variance is not 30, then adjustments must be made to bring it under control. On a given day, an analyst at the company records the inventory of hinges at 26 randomly selected times. The variance of the sample is calculated to be 49.38. Conduct a hypothesis test at the a = 0.05 significance level to find out if the population variance of hinges is different than 30. Based on your results, do adjustments need to be made