Please follow directions and answer both the questions with details

Directions

Question 1

Question 2

For each problem, show at minimum: 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 y? test test statistics to three decimals; round Ftest 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 p-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 you 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 40. If the variance is not 40, 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 28 randomly selected times. The variance of the sample is calculated to be 64.98. Conduct a hypothesis test at the a = 0.05 significance level to find out if the population variance of hinges is different than 40. Based on your results, do adjustments need to be made? 2. (14 points) A hand cream company was interested in whether customers' preferences for hand cream are related to their parental status. On a recent survey of a random sample of 306 customers, the company asked: "Do you have children under five years of age that live with you?" The customer answered "Yes" if they had children under 5 years of age, and "No" if they did not. The customers were also asked: "What is the most important characteristic you consider when choosing a hand cream?" The answer choices were: nice scent; long- lasting; non-greasy; and all-natural The company would like you to perform a Test of Independence to determine if hand cream preference is related to parental status, at the a = 0.10 significance level. Is there evidence that these two variables are related in the population of customers? The observed frequencies from the sample are given in the following table: Observed Frequencies (0) Children under 5 at home? Row Total Hand Cream Preference nice scent Yes 50 No 37 long-lasting 25 36 non-greasy 35 40 all-natural 48 35 Column Total Here is the calculation table for the Chi-Square test statistic Here is the calculation table for the Chi-Square test statistic: Children at home Yes Observed Frequency Preference nice scent Expected Frequency Difference squared/Expected nice scent No Yes long-lasting long-lasting No non-greasy Yes non-greasy No all-natural Yes all-natural No Xiest After you calculate and fill out the tables, write the four steps for the hypothesis test on the next page. You need only report the test statistic in Step 2, since the calculation is shown at length above