Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 28, 31, 40, 37, 26, 38. Use a 0.01 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die? Click here to view the chi-square distribution table. The test statistic is (Round to three decimal places as needed.) The critical value is (Round to three decimal places as needed.) State the conclusion. Ho- There sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes to be equally likely, so the loaded die to behave differently from a fair die.A data set lists weights (lb) of plastic discarded by households. The highest weight is 5.52 lb, the mean of all of the weights is x = 2.055 lb, and the standard deviation of the weights is s = 1.329 lb. a. What is the difference between the weight of 5.52 lb and the mean of the weights? b. How many standard deviations is that [the difference found in part (a)]? c. Convert the weight of 5.52 lb to a z score. d. If we consider weights that convert to z scores between - 2 and 2 to be neither significantly low nor significantly high, is the weight of 5.52 lb significant? a. The difference is |lb. (Type an integer or a decimal. Do not round.) b. The difference is |standard deviations. (Round to two decimal places as needed.) c. The z score is z = (Round to two decimal places as needed.) d. The highest weight is significantly low. not significant. significantly high.Chi-square distribution table X Area to the Right of the Critical Value Degrees of Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.001 0.004 0.016 2.706 0.010 0.020 0.051 0.103 0.211 4.605 0.072 0. 115 0.216 0.352 0.584 6.251 0.207 0.297 0.484 0.711 1.064 7.779 0.412 0.554 0.831 1.145 1.610 9.236 -6 0 V Q UI A W N 0.676 0.872 1.237 1.635 2.204 10.645 0.989 1.239 1.690 2.167 2.833 12.017 1.344 1.646 2. 180 2.733 3.490 13.362 1.735 2.088 2.700 3.325 4. 168 14.684 2. 156 2.558 3.247 3.940 4.865 15.987 Print DoneHere are summary statistics for randomly selected weights of newborn girls: n = 36, x = 3227.8 g, s = 686.4 g. Use a confidence level of 99% to complete parts (a) through (d) below. a. Identify the critical value to /2 used for finding the margin of error. ta /2 = (Round to two decimal places as needed.) b. Find the margin of error. E = 9 (Round to one decimal place as needed.) c. Find the confidence interval estimate of H. g